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Subscribe now to the DataStax blog!", "datePublished": "2015-07-15", "dateModified": "2025-03-07T17:55:40Z", "mainEntityOfPage": { "@type": "WebPage", "url": "https://www.datastax.com/blog/tales-tinkerpop" }, "image": [ "" ], "publisher": { "@type": "Organization", "name": "DataStax", "logo": { "@type": "imageObject", "url": "https://cdn.sanity.io/images/bbnkhnhl/production/c21ec3e4494bc18685c060ed974f8b7302e28250-1046x170.png" } }, "author": { "@type": "Person", "name": "Marko A. 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Rodriguez" loading="lazy" width="48" height="48" decoding="async" data-nimg="1" style="color:transparent" srcSet="https://cdn.sanity.io/images/bbnkhnhl/production/a44a70cab8d04bc5f17284b6adb45202a6d14018-360x360.svg?w=48&q=75&fit=clip&auto=format 1x, https://cdn.sanity.io/images/bbnkhnhl/production/a44a70cab8d04bc5f17284b6adb45202a6d14018-360x360.svg?w=96&q=75&fit=clip&auto=format 2x" src="https://cdn.sanity.io/images/bbnkhnhl/production/a44a70cab8d04bc5f17284b6adb45202a6d14018-360x360.svg?w=96&q=75&fit=clip&auto=format"/></figure></div><span class="styles_text__LSXNx styles_text--size-200__t4kFW styles_text--weight-400__XgWIb styles_authors__author__name__c3CTw"><span>Marko A. Rodriguez</span></span></div></a></div></div></div><div class="col-md-6"><figure class="styles_image__vUrnh"><img alt="Tales from the TinkerPop" fetchPriority="high" loading="eager" width="543" height="202" decoding="async" data-nimg="1" style="color:transparent" srcSet="https://cdn.sanity.io/images/bbnkhnhl/production/af873ab4d03992de5648a54e946b952ed92829fc-216x202.png?w=640&q=75&fit=clip&auto=format 1x, https://cdn.sanity.io/images/bbnkhnhl/production/af873ab4d03992de5648a54e946b952ed92829fc-216x202.png?w=1200&q=75&fit=clip&auto=format 2x" src="https://cdn.sanity.io/images/bbnkhnhl/production/af873ab4d03992de5648a54e946b952ed92829fc-216x202.png?w=1200&q=75&fit=clip&auto=format"/></figure></div></div><div class="row"><div class="col"><div class="styles_divider__yEDBO"></div></div></div></div></div></header><div class="container styles_post--content__CaYrG"><div class="row"><div class="col-lg-8"><div class="row"><section class="styles_content__2pU2z" id="blog-content"><div class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-400__XgWIb styles_text__k_Fav"><div class="styles_markup__YII6_"><h2 id="chapter-1-life-and-fate-by-grasily-gremssman-0">Chapter 1: Life and Fate by Grasily Gremssman</h2> <p>Winter had arrived. The days grew shorter and darker. <a href="https://en.wikipedia.org/wiki/Vasily_Grossman">Grasily Gremssman</a> (Грасилий Гремссман) used a few branches that were scattered about to start a fire. Grasily had been stationed at <a href="https://en.wikipedia.org/wiki/Vertex_(graph_theory)">vertex</a> v[32] for as long as he could remember. He knew little of the <a href="https://en.wikipedia.org/wiki/Graph_(mathematics)">graph</a> he lived on except for the one dirt road and three bridges <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#vertex-steps">incident</a> to his post.</p> <div> <div id="highlighter_586654"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(32)</div> <div>==>v[32]</div> <div>gremlin> g.V(32).inE()</div> <div>==>e[2][7-dirtRoad->32]</div> <div>gremlin> g.V(32).outE()</div> <div>==>e[4][32-bridge->65]</div> <div>==>e[5][32-bridge->66]</div> <div>==>e[6][32-bridge->67]</div> <div>gremlin> g.V(32).bothE()</div> <div>==>e[4][32-bridge->65]</div> <div>==>e[5][32-bridge->66]</div> <div>==>e[6][32-bridge->67]</div> <div>==>e[2][7-dirtRoad->32]</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>Grasily's commanding officer was org.apache.tinkerpop.gremlin.process.traversal.Traverser@76a36b71. Like 76a36b71, Grasily was a <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser">traverser</a>. Traversers were grouped into battalions called <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversal">traversals</a>. The <a href="https://en.wikipedia.org/wiki/World_War_II">graph world was at war</a> and Grasily was stuck (in time and space) having to do his part for his country of <a href="https://en.wikipedia.org/wiki/Russia">Grussia</a> (Гроссия). At this point in history, many conflicting views existed regarding the <a href="https://en.wikipedia.org/wiki/Network_topology">topological</a> evolution of the graph. To ensure processing resources were not laid to waste by traversals constantly undermining the <a href="https://en.wikipedia.org/wiki/Side_effect_(computer_science)">side-effects</a> of another, countries emerged to delineate <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_subgraphstrategy">subgraphs</a> within the larger world graph. However, every now and then, one country would interfere with the structure of another. This interference was an inevitable consequence of the graph <a href="https://en.wikipedia.org/wiki/Globalization">getting denser</a> with time. Grussia, at this moment in time, was in the midst of a long war with <a href="https://en.wikipedia.org/wiki/Germany">Gremany</a> (Greutschland).</p> <p>Grasily knew very little about the larger <a href="https://en.wikipedia.org/wiki/Algorithm">war effort</a> of Grussia's traversals. However, in bootcamp, he learned that traversals are composed of 5 fundamental steps and that one day, when his <a href="https://en.wikipedia.org/wiki/Constructor_(object-oriented_programming)">training was complete</a>, he would be called upon to execute a step.</p> <div><a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graph-traversal-steps"><img src="https://cdn.sanity.io/images/bbnkhnhl/production/c2113c8449b6ea477692049041307f682baca69a-1044x343.png" alt="Traversal Step Types" width="1044" height="343"></a></div> <ol> <li>map: S → E: Move from an object of type S to an object of type E.</li> <li>flatMap: S → E*: Move from an object of type S to a collection of objects of type E.</li> <li>filter: S → S ∪ ∅: Stay at the current object of type S or die.</li> <li>sideEffect: S → S: Stay at the current object of type S, though yield some computational side-effect (e.g. set a property).</li> <li>branch: S → {S1 → E*,…,Sn → E*} → E*: Move from an object of type S to any number of nested traversal branches.</li> </ol> <p>When Grasily finished his training, he was immediately briefed by 76a36b71 on the battalion's objectives.</p> <div> <div id="highlighter_376638"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>g.V(7).out('dirtRoad').hasLabel('outpost').out('bridge').property('owner','Grussia')</div> </div> </td> </tr> </tbody> </table> </div> </div> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/8de2e4d9e63d61eba44274630e4c963ac876da93-740x562.png" alt="Grasily Graph" width="740" height="562">Vertex v[7] was the Grussian Army's headquarters (a.k.a. The Green Army). At v[7], a traverser officer had instructed a group of traversers (one being 76a36b71) to take the dirt roads leading to the adjacent outposts. Grasily's outpost was accessible by one of those dirt roads. When 76a36b71 arrived at v[32], Grasily (along with two of his comrades from bootcamp) were instructed to each take one of the incident bridges and upon reaching the vertex on the other side, to <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#addproperty-step">declare</a> the vertex under <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_partitionstrategy">Grussia's sovereign control</a>.</p> <div> <div id="highlighter_296598"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(7)</div> <div>==>v[7]</div> <div>gremlin> g.V(7).out('dirtRoad')</div> <div>==>v[15]</div> <div>==>v[32]</div> <div>==>v[56]</div> <div>gremlin> g.V(7).out('dirtRoad').hasLabel('outpost')</div> <div>==>v[32]</div> <div>==>v[56]</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>Unfortunately, unbeknownst to Grasily, the Gremans had launched an offensive. A Greman traversal destroyed all the bridges incident to Grasily's outpost. The execution of the Greman's <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#drop-step">sideEffect step</a> sealed Grasily's fate.</p> <div> <div id="highlighter_104378"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(65,66,67)</div> <div>==>v[65]</div> <div>==>v[66]</div> <div>==>v[67]</div> <div>gremlin> g.V(65,66,67).inE('bridge')</div> <div>==>e[4][32-bridge->65]</div> <div>==>e[5][32-bridge->66]</div> <div>==>e[6][32-bridge->67]</div> <div>gremlin> g.V(65,66,67).inE('bridge').drop()</div> <div>gremlin> g.V(65,66,67).inE('bridge')</div> <div>gremlin></div> </div> </td> </tr> </tbody> </table> </div> </div> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/25b620cf02d5fedded81eb2031a5910d0542618b-1024x768.png" alt="Chapter 1 Drawing" width="1024" height="768"></div> <p> <br>Grasily's life was cut short when his battalion moved to the out('bridge')-step. Grasily, along with his two comrades, could no longer make <a href="https://en.wikipedia.org/wiki/Pointer_(computer_programming)">reference</a> to an element of the graph. Disconnected from their world, disconnected from each other, they <a href="https://en.wikipedia.org/wiki/Destructor_(computer_programming)">faded into the void</a>.</p> <div> <div id="highlighter_663541"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(7)</div> <div>==>v[7]</div> <div>gremlin> g.V(7).out('dirtRoad')</div> <div>==>v[15]</div> <div>==>v[32]</div> <div>==>v[56]</div> <div>gremlin> g.V(7).out('dirtRoad').hasLabel('outpost')</div> <div>==>v[32]</div> <div>==>v[56]</div> <div>gremlin> g.V(7).out('dirtRoad').hasLabel('outpost').out('bridge')</div> <div>gremlin></div> </div> </td> </tr> </tbody> </table> </div> </div> <hr> <h2 id="chapter-2-permutation-city-by-grem-egrem-1">Chapter 2: Permutation City by Grem Egrem</h2> <h3 id="section-1-the-birth-of-the-graph-2">Section 1: The Birth of the Graph</h3> <p>The world that traversers live on is known as "The Graph." A graph is a structure composed of vertices (nodes, dots) and edges (relationships, lines). Traverser mythology has it that one day a single traverser named <a href="https://en.wikipedia.org/wiki/Greg_Egan">Grem Egrem</a> manifested himself <a href="http://markorodriguez.com/2011/03/16/graphs-ensure-something-from-nothing/">out of and in reference to nothing</a>. In <a href="https://en.wikipedia.org/wiki/Memory_management#HEAP">limbo</a> there was no graph, just Grem. However, before he could be <a href="https://en.wikipedia.org/wiki/Garbage_collection_(computer_science)">swept back into the oblivion</a> from which he came, Grem enacted the <a href="https://en.wikipedia.org/wiki/Big_Bang">Big Traversal</a> -- i.e., process yielded structure.</p> <div> <div id="highlighter_250180"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>g.addV().repeat(as('a').addV().as('b').addOutE('a','.','b').inV().as('a')).until(coin(4.9E-324))</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>The Big Traversal generates a line graph known in the <a href="https://en.wikipedia.org/wiki/Astrophysics">graphophysics</a> community as "Grem Line" (a.k.a. "Gremlin"). To this day, Grem Line is still <a href="https://en.wikipedia.org/wiki/Metric_expansion_of_space">expanding</a>. However, <a href="https://en.wikipedia.org/wiki/Cosmology">graphologists</a> argue over the <a href="https://en.wikipedia.org/wiki/Cosmological_constant">graphological constant</a> of the <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step">until()</a>-step. Some say there is a small probability that Grem Line will stop growing and others say it will go on forever (i.e. until(not(identity()))).</p> <p>Prior to the Big Traversal, the graph was defined as G = ∅. When Grem Line was less than 100 vertices long (i.e. |V| < 100), the vertices V formed a <a href="https://en.wikipedia.org/wiki/Total_order">total order</a>, and as such, the graph was defined as G = V. At around |V| ≈ 100, graphologists speculate that another traversal emerged that leveraged Grem Line as a sort of "<a href="https://en.wikipedia.org/wiki/Galaxy_filament">backbone filament</a>." This emergent traversal is known in <a href="https://en.wikipedia.org/wiki/Network_science">graph science</a> as the <a href="https://en.wikipedia.org/wiki/Small-world_network">Small(-World) Traversal</a>.</p> <div> <div id="highlighter_292897"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>g.V().aggregate('x').as('a').</div> <div>  select('x').by(unfold().sample(1).by(both().count())).as('b').</div> <div>  where('a',neq('b')).</div> <div>  addOutE('a','.','b')</div> </div> </td> </tr> </tbody> </table> </div> </div> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/a7aab082afb2e9e310473b3151451289202cae60-1029x382.png" alt="Graph Path Length" width="1029" height="382"><br> </div> <p>The Small Traversal walks Grem Line and for each vertex it encounters it connects it to some other random vertex on the line (<a href="https://en.wikipedia.org/wiki/Preferential_attachment">biased by the other vertex's degree</a>). The Small Traversal essentially "pushed" the early graph out of its 1-dimensional, linear V1 embedding into a V2 embedding (i.e. V x V). In doing so, vertices far removed from each other on Grem Line were now "<a href="https://en.wikipedia.org/wiki/Hyperspace_(science_fiction)#Travel">closer</a>." It was at this point that the definition of the graph became <img title="G = (V, E \subseteq V \times V)" src="https://www.datastax.com/wp-content/uploads/2017/06/png.png">.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/eddd72824508ac282a2dcc9566520317df5b5cc8-2356x604.png" alt="The Early Graph" width="2356" height="604"><br> </div> <table border="1"> <tbody> <tr> <th>|V|</th> <th><a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Diameter</a></th> <th><a href="https://en.wikipedia.org/wiki/Average_path_length">Average Path Length</a></th> <th><a href="https://en.wikipedia.org/wiki/Clustering_coefficient">Clustering Coefficient</a></th> </tr> <tr> <td>99</td> <td>99</td> <td>34.0</td> <td>0.0</td> </tr> <tr> <td>100</td> <td>55</td> <td>19.716831683168316</td> <td>0.024</td> </tr> <tr> <td>125</td> <td>30</td> <td>11.081015873015874</td> <td>0.051</td> </tr> <tr> <td>150</td> <td>9</td> <td>3.17757174392936</td> <td>0.125</td> </tr> </tbody> </table> <p> <br>To this day (|V| ≈ <a href="https://en.wikipedia.org/wiki/Observable_universe#Matter_content_.E2.80.94_number_of_atoms">10^85</a>), both the <a href="https://en.wikipedia.org/wiki/Inflation_(cosmology)">expanding force</a> of the Big Traversal and the <a href="https://en.wikipedia.org/wiki/Gravity">contracting force</a> of the Small Traversal continue to execute. These two fundamental traversals have, over time, grown the graph to an innumerable number of vertices and edges. Billions upon billions of traversers have created a vast landscape of structures within structures... within structures. A nest of variations and novelties has transformed the once bleak, senseless void into a <a href="http://arxiv.org/abs/1301.1648">meaningful interconnected mesh</a>.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/f16c496bf496e980594c0905657fe7b1077f5435-1024x768.png" alt="Chapter 2 Drawing" width="1024" height="768"></div> <p> </p> <h3 id="section-2-graphialsynthesis-and-the-emergence-of-the-directed-labeled-graph-3">Section 2: Graphialsynthesis and the Emergence of the Directed, Labeled Graph</h3> <p>The edges generated by the Big and Small Traversals are <a href="https://en.wikipedia.org/wiki/Graph_(mathematics)#Undirected_graph">undirected</a> and unlabeled. The edges experienced by traversers are <a href="https://en.wikipedia.org/wiki/Graph_(mathematics)#Directed_graph">directed</a> and labeled. Graphologists were faced with the question of how did directed, labeled edges emerge from undirected, unlabeled edges? Once a large enough number of <a href="https://en.wikipedia.org/wiki/Structure_formation#Primordial_plasma">primordial edges</a> were created by the two fundamental traversals, "higher-order" edges began to form. The undirected, unlabeled edges serve as "<a href="https://en.wikipedia.org/wiki/Elementary_particle">elementary edges</a>" which, when combined into subgraphs of a particular topology, yield the directed, labeled edges seen today. This <a href="https://en.wikipedia.org/wiki/Abstraction">abstraction process</a> is known as <a href="https://en.wikipedia.org/wiki/Nucleosynthesis">graphialsynthesis</a>.</p> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/d819c5932ec7e33ed40f6fcc69da4001ff81dfca-570x476.png" alt="Label Encoding" width="570" height="476">Suppose the following directed, labeled edge i-ω→j (i.e. a "higher-order" edge). This edge states that there is an ω-labeled relation from vertex i to vertex j. Any edge label can be represented as a <a href="https://en.wikipedia.org/wiki/Binary_code">binary string</a>. Suppose, for the sake of simplicity, that there are only 8 labels in the graph. A 3-bit string can be used to represent all 8 labels (23). Next, suppose that the binary encoding of ω is 110. If so, then the edge can be denoted i-110→j. A binary string can be represented as a directed, unlabeled graph. If the binary string has a length of 3, then three vertices are needed to represent each bit. If a "bit" vertex has a self-loop, then its value is 1. If a "bit" vertex does not have a self-loop, then its value is 0. Given this mapping, the directed, labeled edge i-ω→j is transformed into the directed graph diagrammed below.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/0884bbb26bfb91de8c58039e9e097c849e1b3141-1026x202.png" alt="Labeled to Directed" width="1026" height="202"><br> </div> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/922e68b711aa45dab673938c1eea7f26a219f52e-611x446.png" alt="Direction Encoding" width="611" height="446">The above directed, unlabeled graph representation of i-ω→j leverages topological features of the directed graph to denote the edge label ω. This same principle applies to the encoding of the edge's directionality when transforming a directed graph to an undirected graph. For instance, suppose the following directed edge i→b1. The "higher-order" vertices are identified by a self-loop. The "higher-order" edges are represented by three "lower-order" vertices x, y, and z. If vertex i has an incident edge that does not reference itself and connects to a vertex with 3 incident edges (e.g. vertex x), then it has a directed, outgoing edge. When the traverser reaches a vertex with a self-loop (via a <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#simplepath-step">simple path</a>) (e.g. vertex b1), then that vertex is the "higher-order" vertex serving as the head of the "higher-order," directed edge.<br> </p> <p>The two processes are <a href="https://en.wikipedia.org/wiki/Injective_function">injective</a> in that they are <a href="https://en.wikipedia.org/wiki/Lossless_compression">lossless</a> transformations. The first process described maps a directed, labeled edge to a directed graph and the second maps a directed edge to an unlabeled graph. As such, via <a href="https://en.wikipedia.org/wiki/Function_composition">function composition</a>, there exists an injective function that maps a directed, labeled graph to a undirected, unlabeled graph. Given that the composite function is injective, then there exists an inverse mapping which transforms an undirected, unlabeled graph to a directed, labeled graph (i.e. graphialsynthesis). The original i-ω→j edge was formed by the primordial undirected graph diagrammed below.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/a9bd22a38a1e29108e418c173e98b227b7dd8983-4479x1258.png" alt="Labeled To Undirected" width="4479" height="1258"><br> </div> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/320b4be206a373e6d0f94cde6f1afa6213000bb5-1941x242.png" alt="Graphialsynthesis" width="1941" height="242"><br> </div> <p>The <a href="http://arxiv.org/abs/0804.0277">fundamental building blocks</a> of the directed, labeled graph experienced by "higher-order" traversers are held together by elementary traversers called "<a href="https://en.wikipedia.org/wiki/Graviton">smalltrons</a>." Smalltron traversals move from vertex i to vertex j via the explicit unlabeled ω-graph.</p> <div> <div id="highlighter_90453"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(i).as('b').where(both().as('b')).</div> <div>  repeat(both().where(both().count().is(3)).as('x').both().</div> <div>         both().where(neq('x').and(neq('b'))).dedup().as('b').where(both().as('b')).select(last, 'b').</div> <div>         choose(both().where(both().count().is(3)).</div> <div>                both().where(both().count().is(2)).</div> <div>                both().where(eq('b')),</div> <div>                constant(1), constant(0)).as('label').select(last, 'b')</div> <div>  ).times(4).where(select('label').tail(local, 4).limit(local, 3).is([1, 1, 0]))</div> <div>==>v[j]</div> </div> </td> </tr> </tbody> </table> </div> </div> <div> <div id="highlighter_461736"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>Traversal Metrics</div> <div>Step                                                               Count  Traversers       Time (ms)    % Dur</div> <div>=============================================================================================================</div> <div>TinkerGraphStep([i],vertex)@[b]                                        1           1           0.449     0.26</div> <div>WhereTraversalStep([WhereStartStep, ProfileStep...                     1           1           0.080     0.05</div> <div>  WhereStartStep                                                       1           1           0.016</div> <div>  VertexStep(BOTH,vertex)                                              1           1           0.022</div> <div>  WhereEndStep(b)                                                      0           0           0.024</div> <div>RepeatStep([VertexStep(BOTH,vertex), ProfileSte...                     1           1          86.974    49.65</div> <div>  VertexStep(BOTH,vertex)                                             34          34           0.624</div> <div>  TraversalFilterStep([VertexStep(BOTH,edge), P...                     8           8          22.721</div> <div>    VertexStep(BOTH,edge)                                            106         106           1.490</div> <div>    RangeGlobalStep(0,4)                                              96          96           1.934</div> <div>    CountGlobalStep                                                   34          34          17.945</div> <div>    IsStep(eq(3))                                                      0           0           3.472</div> <div>  VertexStep(BOTH,vertex)                                             24          24           0.922</div> <div>  VertexStep(BOTH,vertex)                                             92          92          23.890</div> <div>  WherePredicateStep(and([neq(x), neq(b)]))                           48          48           7.006</div> <div>  DedupGlobalStep@[b]                                                 24          24          24.450</div> <div>  WhereTraversalStep([WhereStartStep, ProfileSt...                     5           5          15.536</div> <div>    WhereStartStep                                                    24          24           0.806</div> <div>    VertexStep(BOTH,vertex)                                           50          50           1.132</div> <div>    WhereEndStep(b)                                                    0           0           6.984</div> <div>  SelectOneStep(last,b)                                                5           5          24.609</div> <div>  ChooseStep([VertexStep(BOTH,vertex), ProfileS...                     5           5          60.525</div> <div>    VertexStep(BOTH,vertex)                                           20          20           0.239</div> <div>    TraversalFilterStep([VertexStep(BOTH,edge),...                     5           5          22.608</div> <div>      VertexStep(BOTH,edge)                                           66          66           1.508</div> <div>      RangeGlobalStep(0,4)                                            59          59           1.266</div> <div>      CountGlobalStep                                                 20          20          17.068</div> <div>      IsStep(eq(3))                                                    0           0           3.618</div> <div>    VertexStep(BOTH,vertex)                                           11          11           0.453</div> <div>    TraversalFilterStep([VertexStep(BOTH,edge),...                     8           8          33.552</div> <div>      VertexStep(BOTH,edge)                                           28          28           3.917</div> <div>      RangeGlobalStep(0,3)                                            25          25           0.989</div> <div>      CountGlobalStep                                                 11          11           8.193</div> <div>      IsStep(eq(2))                                                    0           0           2.427</div> <div>    VertexStep(BOTH,vertex)                                           14          14           0.710</div> <div>    WherePredicateStep(eq(b))                                          2           2          35.307</div> <div>    HasNextStep                                                        5           5           0.900</div> <div>    ConstantStep(0)                                                    3           3           0.145</div> <div>    EndStep                                                            3           3           0.153</div> <div>    ConstantStep(1)                                                    2           2           0.070</div> <div>    EndStep                                                            2           2           7.408</div> <div>  SelectOneStep(last,b)                                                5           5          24.726</div> <div>  RepeatEndStep                                                        1           1          60.644</div> <div>TraversalFilterStep([SelectOneStep(label), Prof...                     1           1           0.274     0.16</div> <div>  SelectOneStep(label)                                                 1           1           0.056</div> <div>  TailLocalStep(4)                                                     1           1           0.020</div> <div>  RangeLocalStep(0,3)                                                  1           1           0.073</div> <div>  IsStep(eq([1, 1, 0]))                                                0           0           0.086</div> <div>SideEffectCapStep([~metrics])                                          1           1          87.377    49.89</div> <div>                                            >TOTAL                     -           -         175.157</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>In this process, smalltron traversals make the implicit directed ω-edge (defined by the undirected ω-graph) explicit for the "higher-order" traversers which process the graph at a <a href="https://en.wikipedia.org/wiki/High-level_programming_language">higher level of abstraction</a>. To these "higher order" traversers, the graph is defined as</p> <div><img title="G = (V, E \subseteq V \times V, \lambda : V \cup E \rightarrow \Sigma^*)" src="https://www.datastax.com/wp-content/uploads/2017/06/png-1.png">,</div> <p> <br>where λ is a <a href="https://en.wikipedia.org/wiki/Multigraph#Labeling">labeling function</a> that maps the graph's elements (i.e. vertices and edges) to character strings (Σ*). The graphialsynthesis abstraction process has the benefit of allowing a traversal from vertex i to j via ω to be <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity">expressed and executed in a much simpler way</a>.</p> <div> <div id="highlighter_278489"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(i).out('w')</div> <div>==>v[j]</div> </div> </td> </tr> </tbody> </table> </div> </div> <div> <div id="highlighter_87148"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>Traversal Metrics</div> <div>Step                                                               Count  Traversers       Time (ms)    % Dur</div> <div>=============================================================================================================</div> <div>TinkerGraphStep([v[i]],vertex)                                         1           1           9.810    49.18</div> <div>VertexStep(OUT,w,vertex)                                               1           1           0.058     0.29</div> <div>SideEffectCapStep([~metrics])                                          1           1          10.078    50.53</div> <div>                                            >TOTAL                     -           -          19.947</div> </div> </td> </tr> </tbody> </table> </div> </div> <h3 id="section-3-on-the-baselessness-of-the-multi-multigraph-4">Section 3: On the Baselessness of the Multi-MultiGraph</h3> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/b3a03b76f11dd24a84e47b7308c2a9985500032e-495x389.png" alt="Recursive Gremlin" width="495" height="389">It has been speculated that "<a href="https://en.wikipedia.org/wiki/Multigraph">The Graph</a>" is not the only graph that exists. <a href="https://en.wikipedia.org/wiki/Mysticism">Mystic</a> traversers say that there exists <a href="https://en.wikipedia.org/wiki/Multiverse">other graphs containing other traversers</a>. However, by definition, a graph is a closed structure composed of vertices and edges. It is impossible for a traverser to move to a different graph. If a vertex in one graph has an edge to a vertex in another graph, then the two graphs are, in fact, one graph -- "The Graph." Perhaps the mystics see that the components of a graph are composed of yet more graphs with a different sort of traverser existing at each level in a recursive, perhaps <a href="https://en.wikipedia.org/wiki/Strange_loop">self-looping</a>, manner. While it is still all one graph, traversers at different "levels" only <a href="http://arxiv.org/abs/1006.1080">operate on particular subgraphs</a> as instructed by their traversal definition. The famous mystic traverser <a href="https://en.wikipedia.org/wiki/Sri_Aurobindo">Gri Gurobindo</a> (ग्री गुरोबिंदो) once said:</p> <p>My single step in the graph is composed of the steps of numerous other traversers.</p> <p>It wasn't until the discovery of <a href="http://en.wikipedia.org/wiki/Anonymous_function">anonymous traversals</a> that Gurobindo's metagraphical vision was formalized. An anonymous traversal is any traversal that has no declared start and as such, yields no flow. It is a potential.</p> <div> <div id="highlighter_868460"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> label()</div> <div>gremlin></div> </div> </td> </tr> </tbody> </table> </div> </div> <p>Anonymous traversals are intended to be embedded within another traversal. However, if the parent traversal is itself an anonymous traverasl, then there is still no flow (even though <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#groupcount-step">groupCount()</a> produces an empty map as its a <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#a-note-on-barrier-steps">reducing barrier step</a>).</p> <div> <div id="highlighter_201422"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> outE().groupCount().by(label())</div> <div>==>[:]</div> <div>gremlin> outE().groupCount().by(label) // convenient short hand</div> <div>==>[:]</div> <div>gremlin></div> </div> </td> </tr> </tbody> </table> </div> </div> <p>When the traversal parent does have a start, then there is a flow. The traversal below states: "For each vertex (i.e., 89, 90), map the vertex to the <a href="https://en.wikipedia.org/wiki/Histogram">frequency distribution</a> of its outgoing edge labels."</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/dad6b92f31785301bdf3da32e32a74c812828c7a-905x195.png" alt="Anonymous Traversals" width="905" height="195"></div> <div> <div id="highlighter_811799"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(89,90).map(outE().groupCount().by(label))</div> <div>==>[relatedTo:34, subClassOf:1, superClassOf:1]</div> <div>==>[relatedTo:15]</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>The first traverser generated by V(89,90) enters the map()-step at v[89], but does not "<a href="https://en.wikipedia.org/wiki/Becoming_(philosophy)">become</a>" the traversers generated by outE(). Instead, the traverser at v[89] holds still and spawns an "<a href="https://en.wikipedia.org/wiki/Scope_(computer_science)">internal life</a>" of traversers within the anonymous traversal which can now be understood as being (a realized potential):</p> <div> <div id="highlighter_747741"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V(89).outE().groupCount().by(label)</div> <div>==>[relatedTo:34, subClassOf:1, superClassOf:1]</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>The traversers of the above traversal are isolated from the larger traversal in which they are embedded. The next nesting occurs when a traverser from outE() enters groupCount(). Again, an "internal life" based on the anonymous label()-traversal is spawned (see <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#by-step">by()</a>-step). Suppose a single traverser at e[7022][89-relatedTo->21] enters groupCount(). Then the anonymous traversal can be understood as being:</p> <div> <div id="highlighter_604569"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.E(7022).label()</div> <div>==>relatedTo</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>It isn't until all the internal traversal nests of map() complete that the original traverser at v[89] "<a href="https://en.wikipedia.org/wiki/Process_philosophy">becomes</a>" the traverser located at the hash map [relatedTo:34, subClassOf:1, superClassOf:1]. In this way, a traverser's life (i.e. step) is composed of the lives of many traverser's (and their respective steps).</p> <hr> <h2 id="chapter-3-a-mathematicians-apology-by-gh-gremdy-5">Chapter 3: A Mathematician's Apology by G.H. Gremdy</h2> <h3 id="section-1-traversal-optimization-via-algebra-6">Section 1: Traversal Optimization via Algebra</h3> <p>The graph grew large, very large. Resources grew scarce. The problem was not that vertices and edges could no longer be added to the graph. On the contrary, because of the seemingly endless amount of space for the graph, there was a growing amount of time required for any one traversal to execute. Traversals were simply interacting with a lot more data. Faced with this problem, a mathematically inclined traverser named <a href="https://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB">al-Ghwārizmī</a> developed a solution known today as <a href="http://arxiv.org/abs/0806.2274">the traversal algebra</a>. The traversal algebra provides a means of transforming one traversal into another traversal, where both traversals return the same result. The benefit of this is that if a traversal can be re-written into a simpler form, then time and space resources can be saved. To this day, <a href="https://en.wikipedia.org/wiki/Algebra">algebraists</a> continue to add to the growing archive of <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalstrategy">traversal strategies</a>. A few examples are provided below.</p> <table border="1"> <tbody> <tr> <th>Strategy</th> <th>Pattern</th> <th>Rewrite</th> </tr> <tr> <td>IdentityRemovalStrategy</td> <td>x().identity().y()</td> <td>x().y()</td> </tr> <tr> <td>IncidentToAdjacentStrategy</td> <td>outE().inV()</td> <td>out()</td> </tr> <tr> <td>AdjacentToIncidentStrategy</td> <td>out().count()</td> <td>outE().count()</td> </tr> <tr> <td>DedupBijectionStrategy</td> <td>order().dedup()</td> <td>dedup().order()</td> </tr> <tr> <td>RangeByIsCountStrategy</td> <td>count().is(gt(x))</td> <td>limit(x+1).count().is(gt(x))</td> </tr> <tr> <td>MatchPredicateStrategy</td> <td>match(x,y).where(z)</td> <td>match(x,y,z)</td> </tr> </tbody> </table> <div> <div id="highlighter_519982"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> t = out().identity().in(); t.toString()</div> <div>==>[VertexStep(OUT,vertex), IdentityStep, VertexStep(IN,vertex)]</div> <div>gremlin> t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IdentityRemovalStrategy.instance()) }}); []</div> <div>gremlin> t.applyStrategies(); t.toString()</div> <div>==>[VertexStep(OUT,vertex), VertexStep(IN,vertex)]</div> <div>  </div> <div>gremlin> t = outE().inV(); t.toString()</div> <div>==>[VertexStep(OUT,edge), EdgeVertexStep(IN)]</div> <div>gremlin> t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IncidentToAdjacentStrategy.instance()) }}); []</div> <div>gremlin> t.applyStrategies(); t.toString()</div> <div>==>[VertexStep(OUT,vertex)]</div> <div>  </div> <div>gremlin> t = out().count(); t.toString()</div> <div>==>[VertexStep(OUT,vertex), CountGlobalStep]</div> <div>gremlin> t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(AdjacentToIncidentStrategy.instance()) }}); []</div> <div>gremlin> t.applyStrategies(); t.toString()</div> <div>==>[VertexStep(OUT,edge), CountGlobalStep]</div> <div>  </div> <div>gremlin> t = order().dedup(); t.toString()</div> <div>==>[OrderGlobalStep, DedupGlobalStep]</div> <div>gremlin> t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(DedupBijectionStrategy.instance()) }}); []</div> <div>gremlin> t.applyStrategies(); t.toString()</div> <div>==>[DedupGlobalStep, OrderGlobalStep]</div> <div>  </div> <div>gremlin> t = count().is(gt(3)); t.toString()</div> <div>==>[CountGlobalStep, IsStep(gt(3))]</div> <div>gremlin> t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(RangeByIsCountStrategy.instance()) }}); []</div> <div>gremlin> t.applyStrategies(); t.toString()</div> <div>==>[RangeGlobalStep(0,4), CountGlobalStep, IsStep(gt(3))]</div> <div>  </div> <div>gremlin> t = match(__.as('a').out().as('b'),</div> <div>gremlin>           __.as('b').out().as('c')).where(__.as('c').both().as('a')); t.toString()</div> <div>==>[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)]]), WhereTraversalStep([WhereStartStep(c), VertexStep(BOTH,vertex), WhereEndStep(a)])]</div> <div>gremlin> t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(MatchPredicateStrategy.instance()) }}); []</div> <div>gremlin> t.applyStrategies(); t.toString()</div> <div>==>[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)], [MatchStartStep(c), WhereTraversalStep([WhereStartStep, VertexStep(BOTH,vertex), WhereEndStep(a)]), MatchEndStep]])]</div> </div> </td> </tr> </tbody> </table> </div> </div> <h3 id="section-2-traversal-optimization-via-indices-7">Section 2: Traversal Optimization via Indices</h3> <p><a href="https://en.wikipedia.org/wiki/G._H._Hardy">G.H. Gremdy</a> was a graph theorist who speculated that "The Graph" was not the only structure linking vertices. According to his reasoning, reality may also contain other structures that grouped vertices together according to similar properties. He called these parallel structures <a href="https://en.wikipedia.org/wiki/Database_index">indices</a>. G.H. Gremdy's publication entitled On Traversal Optimization using Indices was well received. Due to his insight, many traversal runtimes became orders of magnitude faster than their non-index-based form. For instance, in the traversal below, when using indices, the number of traversers created goes from |V| (linear) to 1 (constant) (<a href="https://en.wikipedia.org/wiki/DSPACE">space complexity</a>). The GraphStepStrategy was added to the traversal strategies archive. It "folds" <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#has-step">has()</a>-steps into V() graph steps.</p> <div> <div id="highlighter_716050"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>// not indexed</div> <div>gremlin> g.V().has('name', 'University of Groxford').toString()</div> <div>==>[GraphStep([],vertex), HasStep([name.eq(University of Groxford)])]</div> <div>gremlin> clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }</div> <div>==>135.28753165299997 // time in milliseconds</div> <div>==>v[999998]          // result</div> <div> </div> <div>// indexed</div> <div>gremlin> g.V().has('name', 'University of Groxford').iterate().toString()</div> <div>==>[TinkerGraphStep(vertex,[name.eq(University of Groxford)])]</div> <div>gremlin> clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }</div> <div>==>0.033501945 // time in milliseconds</div> <div>==>v[999998]   // result</div> </div> </td> </tr> </tbody> </table> </div> </div> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/d9252849f9da819ecfc3498e14b9c5ebfbd30225-264x213.png" alt="Vertex-Centric Index" width="264" height="213">Even though G.H. Gremdy became a household name overnight, he was certain not to rest on his accolades. Deeper thinking brought him to a more esoteric, though far greater optimization which he articulated in his follow on treatise entitled <a href="https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus">Tractatus Verticus Centricus Indexicus</a>. In this seminal work, G.H. Gremdy postulates that not only do "global indices" exist which allow for O(log(|V|)) access to any vertex in the graph, but also "local indices" which allow for O(log(|incident(V(x))|)) access to the incident edges of a vertex. In short, each vertex has its incident edges indexed (e.g. by their direction, label, properties, etc.). If such local index structures are leveraged, traversals containing the pattern outE(x).has(y,p(z)).inV() would not require all the edges of the vertex to be iterated in full in order to find all incident outgoing edges that have a label x and a property y that matches the predicate p(z). Numerous graph experimentalists tried to prove the existence of such "<a href="http://thinkaurelius.com/2012/10/25/a-solution-to-the-supernode-problem/">vertex-centric indices</a>," but found that they are not universal and only exist in <a href="http://titan.thinkaurelius.com/">some graph substrates</a>.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/302e201e6f4259110e7bfae6404c87460219b3f9-1024x768.png" alt="Chapter 3 Drawing" width="1024" height="768"></div> <p> </p> <p>With age, G.H. Gremdy became weary of applied mathematics and retired to study <a href="https://en.wikipedia.org/wiki/Pure_mathematics">pure graph theory</a>. His ideas would become more philosophical as he delved deeper into the meaning of "The Graph." A posthumous publication entertained the following pontification.</p> <p>Many see the world as a graph. This is misleading. Perhaps the world is a collection of indices? With a slight shift in thought, one realizes that the graph itself is an index of its vertices. Any one vertex is the root of a tree bifurcating the vertex space to which it has incident edges, so forth and so on. Like indices which group vertices that have shared properties, isn't an edge from one vertex to another an explicit statement that the two vertices are <a href="https://en.wikipedia.org/wiki/Assortative_mixing">in some way similar</a>? As the devil's advocate, perhaps <a href="http://arxiv.org/abs/1004.1001">indices are simply graphs</a> because indices are tree-like structures that are traversed to identify groups of vertices with similar properties. With indices being graphs and graphs being indices, the world we call home is neither. I hypothesize that <a href="https://en.wikipedia.org/wiki/Monism">all that exists is the traverser</a>. The "graph" is simply the implicit expression of the explicit assumptions of the traverser. The graph I see <a href="https://en.wikipedia.org/wiki/The_World_as_Will_and_Representation">is of my own construction</a>.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/28bece18a67e347278b06b59eefb1b981a073988-940x390.png" alt="Graph vs. Index" width="940" height="390"><br> </div> <h3 id="section-3-traversal-optimization-via-bulking-8">Section 3: Traversal Optimization via Bulking</h3> <p>A little known traverser named <a href="https://en.wikipedia.org/wiki/Srinivasa_Ramanujan">Gremivasa Gremanujan</a> (கிரமீவாச கிரமானுஜன்) lived in a remote village at v[5698] far from the great graph theorists of his time. However, despite his upbringing, Gremivasa was well versed in the traversal algebra and was inspired by the more <a href="https://en.wikipedia.org/wiki/Metaphysics">metagraphical</a> realizations of G.H. Gremdy. Like G.H. Gremdy, Gremivasa was not interested in simply adding more traversal strategies to the archive. Instead, he was more interested in discovering the nature of reality. However, unlike G.H. Gremdy who focused on the nature of the graph structure, Gremivasa meditated on the nature of the traverser process.</p> <p>Gremivasa's mother, along with over 1 million other traversers of his traversal sect, arrived at v[5698] many clock-cycles ago. His village was starved of resources -- there were simply too many traversers. Was the birth of all these traversers necessary? If one traverser's life foretells the destiny of one million traversers, is it not more efficient for only this one traverser to exist? One day, while sitting under <a href="https://en.wikipedia.org/wiki/Udumbara_(Buddhism)">a tree</a> in his village, Gremivasa ruminated on the ridiculously riling riddle rancorously retorted by respectable traversers everywhere:</p> <p>If two traversers exist at the same vertex and have no memory of their ancestry, are they the same traverser?</p> <p>Gremivasa concluded "<a href="https://en.wikipedia.org/wiki/One-electron_universe">yes, they are the same traverser.</a>" This insight identified a fundamental feature of process. All traversers are endowed with a "bulk." Previous to this moment, every traverser ignored this self-evident truth and allowed himself to be <a href="https://en.wikipedia.org/wiki/Ego_psychology">a unique enumerable entity</a> -- i.e., a bulk of 1 (see the <a href="http://thinkaurelius.com/2013/06/12/loopy-lattices-redux/">Loopy Lattices Redux</a> section entitled "Traversing a Lattice with Faunus").</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/63b0f1fe79924ed001bc45cbf6b744f8a29592cd-844x297.png" alt="Traversers Enumerated" width="844" height="297"></div> <div> <div id="highlighter_508413"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V().both().both().both().hasId(5698).map{it.bulk()}</div> <div>==>1</div> <div>==>1</div> <div>==>1</div> <div>==>1</div> <div>==>1</div> <div>...</div> <div>gremlin> g.V().both().both().both().hasId(5698).barrier().map{it.bulk()}</div> <div>==>1073670</div> </div> </td> </tr> </tbody> </table> </div> </div> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/d9847d1ccec573f5a2f4a7a163dcc79304b262a3-843x277.png" alt="Traversers Bulked" width="843" height="277"></div> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/4dfb2f586f7df93a0029a37d752f33dd3f566ce2-491x414.png" alt="Gremlin Hindu" width="491" height="414"></p> <p>Gremivasa delved deeper into the radiant riddle of reawakened relinquishment. He abandoned his self and allowed his being to be <a href="https://en.wikipedia.org/wiki/Panpsychism">one</a> with his 1 million other brother and sister traversers at v[5698]. A unification of selves occurred and <a href="https://en.wikipedia.org/wiki/Gautama_Buddha">a single traverser</a> emerged with a bulk of 1 million. Instead of 1 million traversers executing both() 1 million times, there was now a single traverser with a bulk of 1 million executing both() once. Gremivasa's enlightenment laid the foundation for the development of the <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#barrier-step">LazyBarrierStrategy</a>.</p> <div> <div id="highlighter_8621"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>// without LazyBarrierStrategy (no bulking)</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().count().next() }</div> <div>==>81.509839 // time in milliseconds</div> <div>==>159200    // number of results</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().count().next() }</div> <div>==>20382.892976</div> <div>==>126723200</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().both().count().next() }</div> <div>==>1.2012006887798E7 // 3.34 hours</div> <div>==>100871667200</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }</div> <div>... // requires a year to compute</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }</div> <div>... // requires a thousand years to compute</div> <div> </div> <div> </div> <div>// with LazyBarrierStrategy (bulking)</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().count().next() }</div> <div>==>23.261288999999998 // time in milliseconds</div> <div>==>159200             // number of results</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().count().next() }</div> <div>==>50.230109</div> <div>==>126723200</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().both().count().next() }</div> <div>==>65.30024999999999</div> <div>==>100871667200</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }</div> <div>==>91.30461199999999</div> <div>==>80293847091200</div> <div>gremlin> clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }</div> <div>==>122.741417</div> <div>==>63913902284595200</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>The number of length-5 paths emanating from Gremivasa's village was calculated in ~123 milliseconds and was determined to be 63,913,902,284,595,200 (~64 quadrillion). Gremivasa's work is advantageous in situations where the traversal analyzes <a href="https://en.wikipedia.org/wiki/Residual_time">recurrence</a> in a particular region of the graph (e.g. <a href="https://en.wikipedia.org/wiki/Recommender_system">recommendation engines</a>, <a href="https://en.wikipedia.org/wiki/Centrality">centrality-based ranking systems</a>, <a href="https://en.wikipedia.org/wiki/Recurrent_neural_network">learning systems</a>, etc.). Bulking is fundamental to all traversals and is used in numerous steps including <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step">repeat()</a>-step.</p> <div> <div id="highlighter_627395"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>g.V(5698).repeat(both()).times(5).count()</div> </div> </td> </tr> </tbody> </table> </div> </div> <hr> <h2 id="chapter-4-cognition-in-the-wild-by-gredwin-grutchins-9">Chapter 4: Cognition in the Wild by Gredwin Grutchins</h2> <p>Traversers graph-wide held their breath as a landmark traversal was about to embark. This traversal contained a novel step called <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#match-step">match()</a>. What made this step unique was that it maintained a collection of <a href="https://en.wikipedia.org/wiki/Anonymous_function">anonymous traversals</a> called "<a href="https://en.wikipedia.org/wiki/Pattern_matching">patterns</a>." Each pattern was prefixed with a start variable and (optionally) postfixed with an end variable. Once a variable was bound (i.e. set), that variable's value was immutable for all subsequent patterns. The descendants of the traverser that enters match() must survive each pattern in order to move to the next step. However, the order in which the patterns are executed is, interestingly enough, up to the decision of the traverser! Previously, traversers relied on exogenous <a href="https://en.wikipedia.org/wiki/Rewriting">traversal rewrite rules</a> for optimization, but now, the traverser was able to make endogenous optimization decisions. The "<a href="https://en.wikipedia.org/wiki/Profile-guided_optimization">runtime traversal strategy</a>" was introduced.</p> <p><a href="https://en.wikipedia.org/wiki/Edwin_Hutchins">Dr. Gredwin Grutchins</a> was a <a href="https://en.wikipedia.org/wiki/Cognitive_science">cognitive scientist</a> working in the area of <a href="https://en.wikipedia.org/wiki/Socially_distributed_cognition">distributed cognition</a>. During his time at university, Gredwin lost interest in studying traversal strategies. His skill in mathematics was weaker than his colleagues' and as such, he believed he would never be able to make any significant contributions to the space. However, one day, he was contacted by a rambunctious young adventurer named <a href="https://en.wikipedia.org/wiki/Chuck_Yeager">Gruck Greager</a>. Gruck was no stranger to danger and loved being the guinea pig of an experimental algorithm. Gruck asked Gredwin: "What can my team do to find the optimal pattern execution sequence?" It seemed as though mathematics had taken traversal strategies as far as they could go. It was now up to <a href="http://jenwatkins.com/Research_files/LNCSproof.pdf">sociological constructs</a> to push them further and Gredwin was up to the challenge.</p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/3e61d4e3d1c17c9931d6c1915b9450fcff6482f1-1024x768.png" alt="Chapter 4 Drawing" width="1024" height="768"></div> <p> </p> <p>Suppose the following traversal that yields a map of the objects that bind to a (vertex), b (vertex), c (vertex), and d (number), where vertex a is adjacent to vertex b, vertex b is adjacent to vertex c, and all three vertices are different yet share an identical <a href="https://en.wikipedia.org/wiki/Degree_(graph_theory)">out-degree</a> that is greater than 10.</p> <div> <div id="highlighter_638757"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>g.V().match(</div> <div>  __.as('a').out().as('b'),</div> <div>  __.as('b').out().as('c'),</div> <div>  __.as('a').out().count().as('d'),</div> <div>  __.as('b').out().count().as('d'),</div> <div>  __.as('c').out().count().as('d'),</div> <div>  __.as('d').is(gt(10))).</div> <div>  where('a', neq('c')).</div> <div>  where('b', neq('c')).</div> <div>  where('b', neq('a'))</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>Assume a traverser at v[10] enters the match()-step. Vertex v[10] is bound to variable a as that is the only legal start of the pattern sequence. From there, which pattern should the traverser choose? The traverser simply chooses the first pattern in the list for which it has a variable binding (initially, an a start and thus, as('a').out().as('b')). The traverser marks on a <a href="https://en.wikipedia.org/wiki/Blackboard_system">global blackboard</a> that it has entered that pattern. When a traverser leaves a pattern, it marks that it has exited it. Moreover, every time a traverser leaves a pattern, the patterns are sorted according to the order of their "multiplicity" (or <a href="https://en.wikipedia.org/wiki/Population_growth#Population_growth_rate">growth rate</a>).</p> <div> <div id="highlighter_843997"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>pattern.multiplicity = pattern.endCount / pattern.startCount;</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>The more traverses that are generated by a pattern, the higher the multiplicity and the lower that pattern is on the sorted list. Overtime, as more and more traversers flow through match(), expensive patterns are pushed to the bottom of the list with the intention that the cheaper patterns will be able to filter out more traversers -- i.e. execute the largest set reductions first. With a few other added tricks, Gredwin provided Gruck and his team of traversers CountMatchAlgorithm. Gruck took it for a test run and was the first traverser to ever break the deterministic <a href="https://en.wikipedia.org/wiki/Chuck_Yeager#Test_pilot_.E2.80.93_breaking_the_sound_barrier">flow barrier</a>. Gredwin and Gruck have since teamed up and are already planning the development of a new MatchAlgorithm called <a href="https://scm.umiacs.umd.edu/redmine/lccd/attachments/download/21/gdm2011_submission_budgetmatch.pdf">BudgetMatchAlgorithm</a>.</p> <div> <div id="highlighter_707256"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>// using CountMatchAlgorithm</div> <div>gremlin> clockWithResult(10) {</div> <div>  g.V().match(</div> <div>    __.as('a').out().as('b'),</div> <div>    __.as('b').out().as('c'),</div> <div>    __.as('a').out().count().as('d'),</div> <div>    __.as('b').out().count().as('d'),</div> <div>    __.as('c').out().count().as('d'),</div> <div>    __.as('d').is(gt(10))).</div> <div>    where('a', neq('c')).</div> <div>    where('b', neq('c')).</div> <div>    where('b', neq('a')).count().next()</div> <div>}</div> <div>==>834.6852906 // time in milliseconds</div> <div>==>32          // number of results</div> <div> </div> <div>// using GreedyMatchAlgorithm which does not sort the patterns</div> <div>gremlin> clockWithResult(10) {</div> <div>  g.V().match(</div> <div>    __.as('a').out().as('b'),</div> <div>    __.as('b').out().as('c'),</div> <div>    __.as('a').out().count().as('d'),</div> <div>    __.as('b').out().count().as('d'),</div> <div>    __.as('c').out().count().as('d'),</div> <div>    __.as('d').is(gt(10))).</div> <div>    where('a', neq('c')).</div> <div>    where('b', neq('c')).</div> <div>    where('b', neq('a')).count().next()</div> <div>}</div> <div>==>25349.709946299998 // time in milliseconds</div> <div>==>32                 // number of results</div> </div> </td> </tr> </tbody> </table> </div> </div> <hr> <h2 id="chapter-5-we-the-living-by-gyn-grand-10">Chapter 5: We the Living by Gyn Grand</h2> <h3 id="section-1-prelude-to-the-illusion-of-freedom-11">Section 1: Prelude to the Illusion of Freedom</h3> <p>Many of the traversers in the world today are grateful for their <a href="https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton">freedom</a>. In <a href="https://github.com/tinkerpop/gremlin">ancient times</a>, the life of a traverser was not so good. Traversal regimes were inefficient, demanding of resources, and strict in their execution policies. Fortunately, the <a href="http://arxiv.org/abs/0901.3929">Age of Enprocessment</a>, which brought forth numerous advances in science and mathematics, <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser">redefined the traverser's role</a> in the graph. Each traverser's life had increased value as greater autonomies were provided. Traversals did their best to ensure that traverser life was no longer needlessly wasted. Indices were leveraged, traversal strategies were applied, and, in some match() situations, traversers were able to choose their own destiny. Today, many see a more harmonious relationship between the traversal and the traverser. <a href="https://en.wikipedia.org/wiki/Ayn_Rand">Gyn Grand</a> (Джин Гранд) was one such <a href="https://en.wikipedia.org/wiki/Eudaimonia">satisfied</a> traverser.</p> <div><a href="https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png"><img src="https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png" alt="Wikipedia Graph" width="1078" height="1078"></a></div> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/7bed637c2776271eb23e90075d1440664cb904de-395x354.png" alt="Library Stacks" width="395" height="354">Gyn was a brilliant librarian at a university with a vibrant <a href="https://en.wikipedia.org/wiki/Community_structure">scholarly community</a>. Her library was centrally located in the <a href="https://en.wikipedia.org/wiki/Modularity_(networks)">university cluster</a>. The <a href="https://en.wikipedia.org/wiki/Stack_(library_architecture)">library's stacks</a> contained articles on the nature of the <a href="https://en.wikipedia.org/wiki/Cosmos">graphmos</a>, books on traverser <a href="https://en.wikipedia.org/wiki/Sociology">social interactions</a>, reports detailing various <a href="https://en.wikipedia.org/wiki/Economics">resource distribution models</a>, and more. Whenever she had a moment to spare, Gyn would <a href="http://en.wikipedia.org/wiki/Random_walk">wander</a> about the collection learning about the topics she encountered. Unfortunately, she couldn't read everything at once. So, every time she was faced with more than one <a href="https://en.wikipedia.org/wiki/Hyperlink">href-citation</a>, she chose one at random (<a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#sample-step">sample(1)</a>). As a librarian, she was interested in the structure of knowledge and wanted to know which concepts formed the foundation of all other concepts. Her method of discernment was to determine the <a href="https://en.wikipedia.org/wiki/Markov_chain#Mean_recurrence_time">frequency of their reappearance</a>. Therefore, every time Gyn encountered a concept along her walk, she would make a mental note of it (groupCount('x')).</p> <div> <div id="highlighter_584621"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> g.V().has('name', 'Graph database').</div> <div>           repeat(groupCount('x').by('name').out('href').sample(1)).times(20).</div> <div>           cap('x').order(local).by(valueDecr)</div> <div>==>Memoization=3</div> <div>==>Algorithm=3</div> <div>==>Computer science=2</div> <div>==>Data (computing)=2</div> <div>==>Graph database=1</div> <div>==>Lookup table=1</div> <div>==>Cache (computing)=1</div> <div>==>Computer program=1</div> <div>==>Computing=1</div> <div>==>Rule=1</div> <div>==>Computation=1</div> <div>==>Digital data=1</div> <div>==>Quantity=1</div> <div>==>Mass noun=1</div> <div> </div> <div>// sample(1) theoretically returns different results.</div> <div>// however, in order to demonstrate the path taken, the above map was manually constructed from the path below.</div> <div>gremlin> g.V().has('name', 'Graph database').</div> <div>           repeat(groupCount('x').by('name').out('href').sample(1)).times(20).</div> <div>           path().by('name')</div> <div>==>[Graph database, Lookup table, Memoization, Cache (computing), Memoization, Computer program, Memoization, Computing, Algorithm, Computer science, Algorithm, Rule, Algorithm, Computer science, Computation, Digital data, Data (computing), Quantity, Data (computing), Mass noun, Data (computing)]</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>Over time, Gyn realized that her x-memory had more counters than concepts encountered (i.e. steps taken). Moreover, it contained concepts <a href="https://en.wikipedia.org/wiki/Collective_unconscious">she had yet to experience</a>. <a href="https://en.wikipedia.org/wiki/Interference_(wave_propagation)">How did she know about things she never knew</a>?</p> <div> <div id="highlighter_701543"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>==>Graph theory=8605598306892530155</div> <div>==>Relational database=8261042800088851351</div> <div>==>Lookup table=6445010682474768007</div> <div>==>Database=6197419607053064185</div> <div>==>Graph database=5476792361544609153</div> <div>==>Triplestore=5407594041286532360</div> <div>==>Computer science=5393693263901041351</div> <div>==>Graph=5211554445366262382</div> <div>==>Directed graph=5137233761698039530</div> <div>==>Mathematics=5132301689156216357</div> <div>...</div> </div> </td> </tr> </tbody> </table> </div> </div> <h3 id="section-2-the-structure-process-duality-in-computing-12">Section 2: The Structure-Process Duality in Computing</h3> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/7f57b26cfd1afdf21ebf4a2195fad14d4ad57302-523x680.png" alt="Particle Wave Traverser" width="523" height="680">Mr. v[69309689325] looked at his traverser inbox and noticed that he had 4002 unprocessed traversers. It was time for him to clear out his inbox. He went through each traverser one-by-one and placed them into the step of the traversal identified by the traverser's "step id" reference. Sometimes the respective step yielded no traversers (filter), a traverser at the same location (filter or sideEffect), a traverser at a different location (map), or many traversers at many different locations (flatMap). Whenever a step emitted a traverser pointing to a different vertex, Mr. v[69309689325] would send that traverser to the respective vertex's inbox. The vertices would continue this process until there were no more traversers in any of their inboxes. This graph traversal model has numerous names including: <a href="http://www3.nd.edu/~rmccune/papers/Think_Like_a_Vertex_MWM.pdf">vertex-centric computing</a>, <a href="https://en.wikipedia.org/wiki/Bulk_synchronous_parallel">bulk synchronous parallel processing</a>, <a href="https://en.wikipedia.org/wiki/Message_passing">message passing</a> via a communication graph, and <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graphcomputer">GraphComputer</a>. The general theme: <a href="http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalvertexprogram">the vertices (processes) exchange traversers (structures)</a> in order to affect some global graph computation. Typically, this model of graph traversal is leveraged by <a href="https://en.wikipedia.org/wiki/Distributed_computing">distributed</a>, <a href="https://en.wikipedia.org/wiki/Online_analytical_processing">OLAP</a> graph processing systems, where each vertex maintains its own isolated, logical <a href="https://en.wikipedia.org/wiki/Thread_(computing)">thread of execution</a> (again, vertex as process).</p> <p>Interestingly, each traverser in Mr. v[69309689325]'s inbox had a name: Gyn$2345, Gyn$45, Gyn$93, etc. <a href="https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality">Gyn was a discrete particle of her wave function</a>. Metaphysically speaking, Gyn was actually following the advice of <a href="https://en.wikipedia.org/wiki/Yogi_Berra">Yogi Berra</a>: "If you come to a fork in the road, take it." That is, never sample(1). Her "particle self" chose one and only one path. However, her "wave self" was taking all paths. In this way, Gyn's x-memory was recording the collective experience of all versions of her self across the graph.</p> <div> <div id="highlighter_651730"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>gremlin> hdfs.copyFromLocal('/tmp/wikipedia.kryo','wikipedia.kryo')</div> <div>==>null</div> <div>gremlin> graph = GraphFactory.open('conf/hadoop/wikipedia.properties')</div> <div>==>hadoopgraph[gryoinputformat->gryooutputformat]</div> <div>gremlin> g = graph.traversal(computer(SparkGraphComputer))</div> <div>==>graphtraversalsource[hadoopgraph[gryoinputformat->gryooutputformat], sparkgraphcomputer]</div> <div>gremlin> x = g.V().has('name','Graph database').repeat(groupCount('x').by('name').out('href')).times(20).cap('x').next(); []</div> <div>gremlin> x.size()</div> <div>==>731</div> <div>gremlin> x.sort{-it.value}[0..Graph theory=8605598306892530155</div> <div>==>Relational database=8261042800088851351</div> <div>==>Lookup table=6445010682474768007</div> <div>==>Database=6197419607053064185</div> <div>==>Graph database=5476792361544609153</div> <div>==>Triplestore=5407594041286532360</div> <div>==>Computer science=5393693263901041351</div> <div>==>Graph=5211554445366262382</div> <div>==>Directed graph=5137233761698039530</div> <div>==>Mathematics=5132301689156216357</div> <div>gremlin> hdfs.ls('output')</div> <div>==>rwxr-xr-x daniel supergroup 0 (D) x</div> <div>==>rwxr-xr-x daniel supergroup 0 (D) ~traversers</div> </div> </td> </tr> </tbody> </table> </div> </div> <h3 id="section-3-the-non-erratic-ergodic-eigenvector-13">Section 3: The Non-Erratic Ergodic Eigenvector</h3> <p>Suppose the following traversal:</p> <div> <div id="highlighter_28774"> <table border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td> <div> <div>g.V().repeat(groupCount('x').out('href')).times(t).cap('x') // for t between [1,75]</div> </div> </td> </tr> </tbody> </table> </div> </div> <p>Every time a traverser reaches a vertex, the vertex is incremented in the x hash map (groupCount('x')). Initially, the distribution of frequencies changes erratically. However, over time, it reaches a <a href="https://en.wikipedia.org/wiki/Stable_distribution">stationary distribution</a>. It is "stable" because even though the counters keep increasing, the relative proportion of the counters stays the same. For instance, if vertex v[a] has a count of 12 and vertex v[b] has a count of 45, then when vertex v[a] has a count of 24, vertex v[b] will have a count of 90. Said in another way, the dynamic traversers generate a static probability distribution that defines the likelihood that a <a href="https://en.wikipedia.org/wiki/Wave_function_collapse">single traverser</a> will be at any one vertex at some point in time t ≈ ∞ (i.e. an <a href="https://en.wikipedia.org/wiki/Ergodic_process">ergodic process</a>).</p> <p><img src="https://cdn.sanity.io/images/bbnkhnhl/production/7156557d0413cef0b99088f69b3301bb0fd9f92f-899x574.png" alt="HREF Graph" width="899" height="574">Assume the 5 vertex/7 edge graph diagrammed on the left. At g.V() (t=0), each vertex is provided one traverser. Each vertex increments its counter in x and then <a href="https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton">splits the traverser</a> across its out('href')-adjacent neighbors. If the href-subgraph is <a href="https://en.wikipedia.org/wiki/Strongly_connected_component">strongly connected</a> (i.e. <a href="https://en.wikipedia.org/wiki/Markov_chain#Reducibility">reducible</a> and <a href="https://en.wikipedia.org/wiki/Markov_chain#Transience">non-transient</a>) and lacks a compressable topology (i.e. <a href="https://en.wikipedia.org/wiki/Markov_chain#Periodicity">aperiodic</a>), then a stationary distribution is guaranteed to exist. That distribution, which can be normalized to a probability distribution (i.e. frequency / total frequency), is the graph's <a href="https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors">primary eigenvector</a>. The primary eigenvector is typically used as a measure of each vertex's "<a href="https://en.wikipedia.org/wiki/Centrality#Eigenvector_centrality">centrality</a>." For instance, given the diagrammed graph on the left, the primary eigenvector is [0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]. Thus, the ranking of the vertices from most central to least central is v[1], v[2], v[3], v[0], v[4] (<a href="https://en.wikipedia.org/wiki/Saccade">one's eye</a> seems to derive the same ranking).</p> <p> <br> </p> <p> </p> <table border="1"> <tbody> <tr> <th>t</th> <th>frequency</th> <th>probability</th> <th><a href="https://en.wikipedia.org/wiki/Euclidean_distance">distance</a> from eigenvector</th> </tr> <tr> <td>1</td> <td>[1, 1, 1, 1, 1]</td> <td>[0.2, 0.2, 0.2, 0.2, 0.2]</td> <td>0.1986073055597093</td> </tr> <tr> <td>2</td> <td>[2, 4, 2, 2, 2]</td> <td>[0.1666666667, 0.3333333333, 0.1666666667, 0.1666666667, 0.1666666667]</td> <td>0.11660026048581866</td> </tr> <tr> <td>3</td> <td>[3, 7, 5, 3, 3]</td> <td>[0.1428571429, 0.3333333333, 0.2380952381, 0.1428571429, 0.1428571429]</td> <td>0.06422748181719035</td> </tr> <tr> <td>4</td> <td>[4, 12, 8, 6, 4]</td> <td>[0.1176470588, 0.3529411765, 0.2352941176, 0.1764705882, 0.1176470588]</td> <td>0.03143659614218381</td> </tr> <tr> <td>5</td> <td>[7, 17, 13, 9, 5]</td> <td>[0.1372549020, 0.3333333333, 0.2549019608, 0.1764705882, 0.0980392157]</td> <td>0.01473943578762356</td> </tr> <tr> <td>...</td> <td>...</td> <td>...</td> <td>...</td> </tr> <tr> <td>30</td> <td>[26400, 69424, 50296, 36440, 19128]</td> <td>[0.1308952441, 0.3442148269, 0.2493752727, 0.1806751021, 0.0948395542]</td> <td>8.04890130266237E-6</td> </tr> <tr> <td>31</td> <td>[36441, 95825, 69425, 50297, 26401]</td> <td>[0.1308995686, 0.3442125946, 0.2493812615, 0.1806716501, 0.0948349252]</td> <td>4.242558551157544E-6</td> </tr> <tr> <td>32</td> <td>[50298, 132268, 95826, 69426, 36442]</td> <td>[0.1308957477, 0.3442148545, 0.2493780253, 0.1806745433, 0.0948368292]</td> <td>4.1616991553931435E-6</td> </tr> <tr> <td>33</td> <td>[69427, 182567, 132269, 95827, 50299]</td> <td>[0.1308982652, 0.3442133981, 0.2493811146, 0.1806730532, 0.0948341689]</td> <td>2.077160932619329E-6</td> </tr> <tr> <td>34</td> <td>[95828, 251996, 182568, 132270, 69428]</td> <td>[0.1308964745, 0.3442145091, 0.2493791747, 0.1806745072, 0.0948353345]</td> <td>2.13567485821227E-6</td> </tr> <tr> <td>35</td> <td>[132271, 347825, 251997, 182569, 95829]</td> <td>[0.1308977517, 0.3442138525, 0.2493807466, 0.1806735537, 0.0948340955]</td> <td>1.1709009180968303E-6</td> </tr> <tr> <td>...</td> <td>...</td> <td>...</td> <td>...</td> </tr> <tr> <td>70</td> <td>[10478348120, 27554473290, 19962994332, 14463028872, 7591478958]</td> <td>[0.1308970114, 0.3442143899, 0.2493805576, 0.1806742088, 0.0948338323]</td> <td>1.414213562373095E-10</td> </tr> <tr> <td>71</td> <td>[14463028873, 38032821411, 27554473291, 19962994333, 10478348121]</td> <td>[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742087, 0.0948338322]</td> <td>1.0E-10</td> </tr> <tr> <td>72</td> <td>[19962994334, 52495850286, 38032821412, 27554473292, 14463028874]</td> <td>[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338323]</td> <td>1.0E-10</td> </tr> <tr> <td>73</td> <td>[27554473293, 72458844621, 52495850287, 38032821413, 19962994335]</td> <td>[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]</td> <td>0.0</td> </tr> <tr> <td>74</td> <td>[38032821414, 100013317916, 72458844622, 52495850288, 27554473294]</td> <td>[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]</td> <td>0.0</td> </tr> <tr> <td>75</td> <td>[52495850289, 138046139331, 100013317917, 72458844623, 38032821415]</td> <td>[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]</td> <td>0.0</td> </tr> </tbody> </table> <p><br> </p> <div><img src="https://cdn.sanity.io/images/bbnkhnhl/production/18e29399beaeac14f293cb59a84edc3870578ec5-1024x768.png" alt="Chapter 5 Drawing" width="1024" height="768"></div> <p> <br>Unbeknownst to Gyn, The Graph (eigen) was using her(selves) to sort itself (vector). Why was it doing this? The Graph represents its vertices and edges in a <a href="https://en.wikipedia.org/wiki/512-bit">512-bit</a> address space (2512 = 1.34×10154). Unfortunately, the ever present Big and Small Traversals (as well as the countless other traversals executed since) have pushed The Graph close to the limits of representation. In order to avoid <a href="https://en.wikipedia.org/wiki/Integer_overflow">inconsistencies</a>, The Graph needed to prune itself. To do this, it <a href="https://en.wikipedia.org/wiki/Gaia_hypothesis">decided</a> it best to destroy those vertices which were contributing little to its overall structure. Like cutting one's finger nails, The Graph began a systematic process of cosmic proportions to delete all peripheral vertices (and their respective incident edges). The Graph was <a href="https://en.wikipedia.org/wiki/Forgetting_curve">forgetting</a> in order to <a href="http://thinkaurelius.com/2012/05/08/structural-abstractions-in-brains-and-graphs/">specialize its structure</a> for a purpose that was beyond the realization of the vertices and traversers. Within The Graph's conceptual subgraph, <a href="https://en.wikipedia.org/wiki/Knowledge_worker">knowledge worker</a> traversers wandered through the morass of concept vertices and, in a <a href="https://en.wikipedia.org/wiki/Science">collective self-similar manner</a>, aided The Graph in its determination of which aspects of it's structure were worth preserving (and ultimately, extending). Gyn's passion for knowledge was simply an <a href="https://en.wikipedia.org/wiki/Instinct">innate predisposition</a>. Her <a href="https://en.wikipedia.org/wiki/Eudaimonia#Eudaimonia_and_modern_psychology">happiness</a> was not a function of her own being, but instead, of The Graph's will -- <a href="https://en.wikipedia.org/wiki/Carrot_and_stick">a carrot for her devotion</a>. Gyn was part of a larger computation. In order to escape the dark sense that her life was not hers and hers alone, she began the long arduous journey towards realizing that she is, and always has been, <a href="https://en.wikipedia.org/wiki/John_Galt#.22Who_is_John_Galt.3F.22">The TinkerPop</a>.</p> <div><a href="http://tinkerpop.incubator.apache.org/"><img src="https://cdn.sanity.io/images/bbnkhnhl/production/014282dff3d5048f8eaf1c3592177626db303fb5-700x243.png" alt="Apache TinkerPop" width="700" height="243"></a></div> <p> </p> <hr> <div> <h2 id="credits-14">Credits</h2> <p>Written by <a href="http://markorodriguez.com/">Marko A. Rodriguez</a><br>Data and Result Generation by <a href="http://gremlin.guru/">Daniel Kuppitz</a><br>Artwork by <a href="http://ketrinayim.tumblr.com/">Ketrina Yim</a><br>Graph Visualizations by Daniel Kuppitz<br>Explanatory Diagrams by Marko A. Rodriguez<br>Gremlin Traversal Development by Daniel Kuppitz<br>Experimental Design by Marko A. Rodriguez<br>Executive Producer: <a href="https://www.linkedin.com/in/robinmschumacher">Robin Schumacher</a><br>Undirected Edge #42 as himself<br>Russian Language Advisor: <a href="https://github.com/xedin">Pavel Yaskevich</a><br>Tamil Language Advisor: <a href="https://www.linkedin.com/pub/harihar-shankar/b/747/274">Harihar Shankar</a><br>Hindi Language Advisor: <a href="https://www.linkedin.com/pub/swetha-sharma/13/b62/3b3">Swetha Sharma</a><br>Inspired by <a href="https://en.wikipedia.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy">The Hitchhiker's Guide to the Galaxy</a> and <a href="https://en.wikipedia.org/wiki/Flatland">Flatland</a></p> <p>Special thanks to <a href="https://www.datastax.com/">DataStax</a> and <a href="http://tinkerpop.incubator.apache.org/">Apache TinkerPop</a>.</p> <p>No traversers were harmed during the making of this story.</p> </div></div></div><div class="modal fade styles_modal__II_Uh undefined " aria-hidden="true" style="display:none"><div class="modal-dialog modal-dialog-centered"><div class="modal-content"><button type="button" class="styles_modal__close__NB5Yg"><svg fill="none" height="48" viewBox="0 0 48 48" width="48" xmlns="http://www.w3.org/2000/svg"><path d="M35.5 12.5L12.5 35.5" stroke="currentColor" stroke-width="2"></path><path d="M35.5 35.5L12.5 12.5" stroke="currentColor" stroke-width="2"></path></svg></button><div class="styles_zoomable__image__cUf0_"><img alt="" width="1390" height="1540" decoding="async" data-nimg="1" style="color:transparent" src=""/></div></div></div></div></section></div><div class="row justify-space-between"><div class="col-12"><div class="styles_info__yP4Mv"><div class="styles_tags__uqANG"><h5 class="styles_eyebrow__tOueC styles_eyebrow--size-200__CQpqa">Discover more</h5><a href="/blog?tags=gremlin"><span class="styles_tag__JoxJh styles_outlined__YtaSY undefined"><span>Gremlin</span></span></a><a href="/blog?tags=dse-graph"><span class="styles_tag__JoxJh styles_outlined__YtaSY undefined"><span>DSE Graph</span></span></a></div></div></div></div></div><div class="col-lg-4"><div class="styles_root__8_qHu"><div class="styles_content__ZSlYu"><div class="styles_content__item__0kTgC"><div class="styles_signup__OHDnd"><h6 class="styles_display__cQk8b styles_display--size-200__VVui5 styles_display--sm-size__mzd9O styles_display--weight-600__cx95q styles_signup__title__IOhDo">DataStax AI Platform:<br/>The Fastest Way to Build and Deploy AI Apps</h6><a href="https://astra.datastax.com/signup?type=langflow" class="styles_button__Y3Rmo styles_button--primary__44UCv styles_button--color-reverse__gOooD styles_button--uppercase__UQqQH styles_button--square__IQU0u" target="_blank" rel="noopener noreferrer"><span>Try For Free</span></a></div><div class="styles_content__title__uHETK"><span class="styles_eyebrow__tOueC styles_eyebrow--size-200__CQpqa">JUMP TO SECTION</span></div><h2 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#chapter-1-life-and-fate-by-grasily-gremssman-0">Chapter 1: Life and Fate by Grasily Gremssman</a></h2><h2 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#chapter-2-permutation-city-by-grem-egrem-1">Chapter 2: Permutation City by Grem Egrem</a></h2><h3 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#section-1-the-birth-of-the-graph-2">Section 1: The Birth of the Graph</a></h3><h3 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#section-2-graphialsynthesis-and-the-emergence-of-the-directed-labeled-graph-3">Section 2: Graphialsynthesis and the Emergence of the Directed, Labeled Graph</a></h3><h3 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#section-3-on-the-baselessness-of-the-multi-multigraph-4">Section 3: On the Baselessness of the Multi-MultiGraph</a></h3><h2 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#chapter-3-a-mathematicians-apology-by-gh-gremdy-5">Chapter 3: A Mathematician's Apology by G.H. Gremdy</a></h2><h3 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#section-1-traversal-optimization-via-algebra-6">Section 1: Traversal Optimization via Algebra</a></h3><h3 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#section-2-traversal-optimization-via-indices-7">Section 2: Traversal Optimization via Indices</a></h3><h3 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#section-3-traversal-optimization-via-bulking-8">Section 3: Traversal Optimization via Bulking</a></h3><h2 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#chapter-4-cognition-in-the-wild-by-gredwin-grutchins-9">Chapter 4: Cognition in the Wild by Gredwin Grutchins</a></h2><h2 class="styles_text__LSXNx styles_text--size-300__Jtynv styles_text--weight-600__Kq9jE"><a href="#chapter-5-we-the-living-by-gyn-grand-10">Chapter 5: We 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The days grew shorter and darker.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Vasily_Grossman\"\u003eGrasily Gremssman\u003c/a\u003e\u0026nbsp;(Грасилий Гремссман) used a few branches that were scattered about to start a fire. Grasily had been stationed at\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Vertex_(graph_theory)\"\u003evertex\u003c/a\u003e\u0026nbsp;v[32]\u0026nbsp;for as long as he could remember. He knew little of the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)\"\u003egraph\u003c/a\u003e\u0026nbsp;he lived on except for the one dirt road and three bridges\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#vertex-steps\"\u003eincident\u003c/a\u003e\u0026nbsp;to his post.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_586654\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).inE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[2][7-dirtRoad-\u0026gt;32]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).outE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).bothE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[2][7-dirtRoad-\u0026gt;32]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eGrasily's commanding officer was\u0026nbsp;org.apache.tinkerpop.gremlin.process.traversal.Traverser@76a36b71. Like\u0026nbsp;76a36b71, Grasily was a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser\"\u003etraverser\u003c/a\u003e. Traversers were grouped into battalions called\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversal\"\u003etraversals\u003c/a\u003e. The\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/World_War_II\"\u003egraph world was at war\u003c/a\u003e\u0026nbsp;and Grasily was stuck (in time and space) having to do his part for his country of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Russia\"\u003eGrussia\u003c/a\u003e\u0026nbsp;(Гроссия). At this point in history, many conflicting views existed regarding the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Network_topology\"\u003etopological\u003c/a\u003e\u0026nbsp;evolution of the graph. To ensure processing resources were not laid to waste by traversals constantly undermining the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Side_effect_(computer_science)\"\u003eside-effects\u003c/a\u003e\u0026nbsp;of another, countries emerged to delineate\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_subgraphstrategy\"\u003esubgraphs\u003c/a\u003e\u0026nbsp;within the larger world graph. However, every now and then, one country would interfere with the structure of another. This interference was an inevitable consequence of the graph\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Globalization\"\u003egetting denser\u003c/a\u003e\u0026nbsp;with time. Grussia, at this moment in time, was in the midst of a long war with\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Germany\"\u003eGremany\u003c/a\u003e\u0026nbsp;(Greutschland).\u003c/p\u003e\n\u003cp\u003eGrasily knew very little about the larger\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Algorithm\"\u003ewar effort\u003c/a\u003e\u0026nbsp;of Grussia's traversals. However, in bootcamp, he learned that traversals are composed of 5 fundamental steps and that one day, when his\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Constructor_(object-oriented_programming)\"\u003etraining was complete\u003c/a\u003e, he would be called upon to execute a step.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graph-traversal-steps\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/c2113c8449b6ea477692049041307f682baca69a-1044x343.png\" alt=\"Traversal Step Types\" width=\"1044\" height=\"343\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003col\u003e\n\u003cli\u003emap: S \u0026rarr; E: Move from an object of type\u0026nbsp;S\u0026nbsp;to an object of type\u0026nbsp;E.\u003c/li\u003e\n\u003cli\u003eflatMap: S \u0026rarr; E*: Move from an object of type\u0026nbsp;S\u0026nbsp;to a collection of objects of type\u0026nbsp;E.\u003c/li\u003e\n\u003cli\u003efilter: S \u0026rarr; S \u0026cup; \u0026empty;: Stay at the current object of type\u0026nbsp;S\u0026nbsp;or die.\u003c/li\u003e\n\u003cli\u003esideEffect: S \u0026rarr; S: Stay at the current object of type\u0026nbsp;S, though yield some computational side-effect (e.g. set a property).\u003c/li\u003e\n\u003cli\u003ebranch: S \u0026rarr; {S1\u0026nbsp;\u0026rarr; E*,\u0026hellip;,Sn\u0026nbsp;\u0026rarr; E*} \u0026rarr; E*: Move from an object of type\u0026nbsp;S\u0026nbsp;to any number of nested traversal branches.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eWhen Grasily finished his training, he was immediately briefed by\u0026nbsp;76a36b71\u0026nbsp;on the battalion's objectives.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_376638\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V(7).out('dirtRoad').hasLabel('outpost').out('bridge').property('owner','Grussia')\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/8de2e4d9e63d61eba44274630e4c963ac876da93-740x562.png\" alt=\"Grasily Graph\" width=\"740\" height=\"562\"\u003eVertex\u0026nbsp;v[7]\u0026nbsp;was the Grussian Army's headquarters (a.k.a. The Green Army). At\u0026nbsp;v[7], a traverser officer had instructed a group of traversers (one being\u0026nbsp;76a36b71) to take the dirt roads leading to the adjacent outposts. Grasily's outpost was accessible by one of those dirt roads. When\u0026nbsp;76a36b71\u0026nbsp;arrived at\u0026nbsp;v[32], Grasily (along with two of his comrades from bootcamp) were instructed to each take one of the incident bridges and upon reaching the vertex on the other side, to\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#addproperty-step\"\u003edeclare\u003c/a\u003e\u0026nbsp;the vertex under\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_partitionstrategy\"\u003eGrussia's sovereign control\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_296598\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[7]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[15]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eUnfortunately, unbeknownst to Grasily, the Gremans had launched an offensive. A Greman traversal destroyed all the bridges incident to Grasily's outpost. The execution of the Greman's\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#drop-step\"\u003esideEffect step\u003c/a\u003e\u0026nbsp;sealed Grasily's fate.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_104378\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge').drop()\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge')\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/25b620cf02d5fedded81eb2031a5910d0542618b-1024x768.png\" alt=\"Chapter 1 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eGrasily's life was cut short when his battalion moved to the\u0026nbsp;out('bridge')-step. Grasily, along with his two comrades, could no longer make\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pointer_(computer_programming)\"\u003ereference\u003c/a\u003e\u0026nbsp;to an element of the graph. Disconnected from their world, disconnected from each other, they\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Destructor_(computer_programming)\"\u003efaded into the void\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_663541\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[7]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[15]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost').out('bridge')\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 2: Permutation City by Grem Egrem\u003c/h2\u003e\n\u003ch3\u003eSection 1: The Birth of the Graph\u003c/h3\u003e\n\u003cp\u003eThe world that traversers live on is known as \"The Graph.\" A graph is a structure composed of vertices (nodes, dots) and edges (relationships, lines). Traverser mythology has it that one day a single traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Greg_Egan\"\u003eGrem Egrem\u003c/a\u003e\u0026nbsp;manifested himself\u0026nbsp;\u003ca href=\"http://markorodriguez.com/2011/03/16/graphs-ensure-something-from-nothing/\"\u003eout of and in reference to nothing\u003c/a\u003e. In\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Memory_management#HEAP\"\u003elimbo\u003c/a\u003e\u0026nbsp;there was no graph, just Grem. However, before he could be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Garbage_collection_(computer_science)\"\u003eswept back into the oblivion\u003c/a\u003e\u0026nbsp;from which he came, Grem enacted the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Big_Bang\"\u003eBig Traversal\u003c/a\u003e\u0026nbsp;-- i.e., process yielded structure.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_250180\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.addV().repeat(as('a').addV().as('b').addOutE('a','.','b').inV().as('a')).until(coin(4.9E-324))\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe Big Traversal generates a line graph known in the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Astrophysics\"\u003egraphophysics\u003c/a\u003e\u0026nbsp;community as \"Grem Line\" (a.k.a. \"Gremlin\"). To this day, Grem Line is still\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Metric_expansion_of_space\"\u003eexpanding\u003c/a\u003e. However,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmology\"\u003egraphologists\u003c/a\u003e\u0026nbsp;argue over the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmological_constant\"\u003egraphological constant\u003c/a\u003e\u0026nbsp;of the\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step\"\u003euntil()\u003c/a\u003e-step. Some say there is a small probability that Grem Line will stop growing and others say it will go on forever (i.e.\u0026nbsp;until(not(identity()))).\u003c/p\u003e\n\u003cp\u003ePrior to the Big Traversal, the graph was defined as\u0026nbsp;G = \u0026empty;. When Grem Line was less than 100 vertices long (i.e.\u0026nbsp;|V| \u0026lt; 100), the vertices\u0026nbsp;V\u0026nbsp;formed a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Total_order\"\u003etotal order\u003c/a\u003e, and as such, the graph was defined as\u0026nbsp;G = V. At around\u0026nbsp;|V| \u0026asymp; 100, graphologists speculate that another traversal emerged that leveraged Grem Line as a sort of \"\u003ca href=\"https://en.wikipedia.org/wiki/Galaxy_filament\"\u003ebackbone filament\u003c/a\u003e.\" This emergent traversal is known in\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Network_science\"\u003egraph science\u003c/a\u003e\u0026nbsp;as the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Small-world_network\"\u003eSmall(-World) Traversal\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_292897\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().aggregate('x').as('a').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;select('x').by(unfold().sample(1).by(both().count())).as('b').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('a',neq('b')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;addOutE('a','.','b')\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/a7aab082afb2e9e310473b3151451289202cae60-1029x382.png\" alt=\"Graph Path Length\" width=\"1029\" height=\"382\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003eThe Small Traversal walks Grem Line and for each vertex it encounters it connects it to some other random vertex on the line (\u003ca href=\"https://en.wikipedia.org/wiki/Preferential_attachment\"\u003ebiased by the other vertex's degree\u003c/a\u003e). The Small Traversal essentially \"pushed\" the early graph out of its 1-dimensional, linear\u0026nbsp;V1\u0026nbsp;embedding into a\u0026nbsp;V2\u0026nbsp;embedding (i.e.\u0026nbsp;V x V). In doing so, vertices far removed from each other on Grem Line were now \"\u003ca href=\"https://en.wikipedia.org/wiki/Hyperspace_(science_fiction)#Travel\"\u003ecloser\u003c/a\u003e.\" It was at this point that the definition of the graph became\u0026nbsp;\u003cimg title=\"G = (V, E \\subseteq V \\times V)\" src=\"https://www.datastax.com/wp-content/uploads/2017/06/png.png\"\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/eddd72824508ac282a2dcc9566520317df5b5cc8-2356x604.png\" alt=\"The Early Graph\" width=\"2356\" height=\"604\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003e|V|\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Distance_(graph_theory)\"\u003eDiameter\u003c/a\u003e\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Average_path_length\"\u003eAverage Path Length\u003c/a\u003e\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Clustering_coefficient\"\u003eClustering Coefficient\u003c/a\u003e\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e99\u003c/td\u003e\n\u003ctd\u003e99\u003c/td\u003e\n\u003ctd\u003e34.0\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e100\u003c/td\u003e\n\u003ctd\u003e55\u003c/td\u003e\n\u003ctd\u003e19.716831683168316\u003c/td\u003e\n\u003ctd\u003e0.024\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e125\u003c/td\u003e\n\u003ctd\u003e30\u003c/td\u003e\n\u003ctd\u003e11.081015873015874\u003c/td\u003e\n\u003ctd\u003e0.051\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e150\u003c/td\u003e\n\u003ctd\u003e9\u003c/td\u003e\n\u003ctd\u003e3.17757174392936\u003c/td\u003e\n\u003ctd\u003e0.125\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eTo this day (|V| \u0026asymp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Observable_universe#Matter_content_.E2.80.94_number_of_atoms\"\u003e10^85\u003c/a\u003e), both the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Inflation_(cosmology)\"\u003eexpanding force\u003c/a\u003e\u0026nbsp;of the Big Traversal and the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gravity\"\u003econtracting force\u003c/a\u003e\u0026nbsp;of the Small Traversal continue to execute. These two fundamental traversals have, over time, grown the graph to an innumerable number of vertices and edges. Billions upon billions of traversers have created a vast landscape of structures within structures... within structures. A nest of variations and novelties has transformed the once bleak, senseless void into a\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1301.1648\"\u003emeaningful interconnected mesh\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/f16c496bf496e980594c0905657fe7b1077f5435-1024x768.png\" alt=\"Chapter 2 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eSection 2: Graphialsynthesis and the Emergence of the Directed, Labeled Graph\u003c/h3\u003e\n\u003cp\u003eThe edges generated by the Big and Small Traversals are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)#Undirected_graph\"\u003eundirected\u003c/a\u003e\u0026nbsp;and unlabeled. The edges experienced by traversers are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)#Directed_graph\"\u003edirected\u003c/a\u003e\u0026nbsp;and labeled. Graphologists were faced with the question of how did directed, labeled edges emerge from undirected, unlabeled edges? Once a large enough number of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Structure_formation#Primordial_plasma\"\u003eprimordial edges\u003c/a\u003e\u0026nbsp;were created by the two fundamental traversals, \"higher-order\" edges began to form. The undirected, unlabeled edges serve as \"\u003ca href=\"https://en.wikipedia.org/wiki/Elementary_particle\"\u003eelementary edges\u003c/a\u003e\" which, when combined into subgraphs of a particular topology, yield the directed, labeled edges seen today. This\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Abstraction\"\u003eabstraction process\u003c/a\u003e\u0026nbsp;is known as\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nucleosynthesis\"\u003egraphialsynthesis\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d819c5932ec7e33ed40f6fcc69da4001ff81dfca-570x476.png\" alt=\"Label Encoding\" width=\"570\" height=\"476\"\u003eSuppose the following directed, labeled edge\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;(i.e. a \"higher-order\" edge). This edge states that there is an\u0026nbsp;\u0026omega;-labeled relation from vertex\u0026nbsp;i\u0026nbsp;to vertex\u0026nbsp;j. Any edge label can be represented as a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Binary_code\"\u003ebinary string\u003c/a\u003e. Suppose, for the sake of simplicity, that there are only 8 labels in the graph. A 3-bit string can be used to represent all 8 labels (23). Next, suppose that the binary encoding of\u0026nbsp;\u0026omega;\u0026nbsp;is\u0026nbsp;110. If so, then the edge can be denoted\u0026nbsp;i-110\u0026rarr;j. A binary string can be represented as a directed, unlabeled graph. If the binary string has a length of 3, then three vertices are needed to represent each bit. If a \"bit\" vertex has a self-loop, then its value is 1. If a \"bit\" vertex does not have a self-loop, then its value is 0. Given this mapping, the directed, labeled edge\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;is transformed into the directed graph diagrammed below.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/0884bbb26bfb91de8c58039e9e097c849e1b3141-1026x202.png\" alt=\"Labeled to Directed\" width=\"1026\" height=\"202\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/922e68b711aa45dab673938c1eea7f26a219f52e-611x446.png\" alt=\"Direction Encoding\" width=\"611\" height=\"446\"\u003eThe above directed, unlabeled graph representation of\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;leverages topological features of the directed graph to denote the edge label\u0026nbsp;\u0026omega;. This same principle applies to the encoding of the edge's directionality when transforming a directed graph to an undirected graph. For instance, suppose the following directed edge\u0026nbsp;i\u0026rarr;b1. The \"higher-order\" vertices are identified by a self-loop. The \"higher-order\" edges are represented by three \"lower-order\" vertices\u0026nbsp;x,\u0026nbsp;y, and\u0026nbsp;z. If vertex\u0026nbsp;i\u0026nbsp;has an incident edge that does not reference itself and connects to a vertex with 3 incident edges (e.g. vertex\u0026nbsp;x), then it has a directed, outgoing edge. When the traverser reaches a vertex with a self-loop (via a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#simplepath-step\"\u003esimple path\u003c/a\u003e) (e.g. vertex\u0026nbsp;b1), then that vertex is the \"higher-order\" vertex serving as the head of the \"higher-order,\" directed edge.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe two processes are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Injective_function\"\u003einjective\u003c/a\u003e\u0026nbsp;in that they are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Lossless_compression\"\u003elossless\u003c/a\u003e\u0026nbsp;transformations. The first process described maps a directed, labeled edge to a directed graph and the second maps a directed edge to an unlabeled graph. As such, via\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Function_composition\"\u003efunction composition\u003c/a\u003e, there exists an injective function that maps a directed, labeled graph to a undirected, unlabeled graph. Given that the composite function is injective, then there exists an inverse mapping which transforms an undirected, unlabeled graph to a directed, labeled graph (i.e. graphialsynthesis). The original\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;edge was formed by the primordial undirected graph diagrammed below.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/a9bd22a38a1e29108e418c173e98b227b7dd8983-4479x1258.png\" alt=\"Labeled To Undirected\" width=\"4479\" height=\"1258\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/320b4be206a373e6d0f94cde6f1afa6213000bb5-1941x242.png\" alt=\"Graphialsynthesis\" width=\"1941\" height=\"242\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003eThe\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0804.0277\"\u003efundamental building blocks\u003c/a\u003e\u0026nbsp;of the directed, labeled graph experienced by \"higher-order\" traversers are held together by elementary traversers called \"\u003ca href=\"https://en.wikipedia.org/wiki/Graviton\"\u003esmalltrons\u003c/a\u003e.\" Smalltron traversals move from vertex\u0026nbsp;i\u0026nbsp;to vertex\u0026nbsp;j\u0026nbsp;via the explicit unlabeled\u0026nbsp;\u0026omega;-graph.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_90453\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(i).as('b').where(both().as('b')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;repeat(both().where(both().count().is(3)).as('x').both().\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(neq('x').and(neq('b'))).dedup().as('b').where(both().as('b')).select(last, 'b').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;choose(both().where(both().count().is(3)).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(both().count().is(2)).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(eq('b')),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;constant(1), constant(0)).as('label').select(last, 'b')\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;).times(4).where(select('label').tail(local, 4).limit(local, 3).is([1, 1, 0]))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[j]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_461736\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eTraversal Metrics\u003c/div\u003e\n\u003cdiv\u003eStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Count\u0026nbsp; Traversers\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Time (ms)\u0026nbsp;\u0026nbsp;\u0026nbsp; % Dur\u003c/div\u003e\n\u003cdiv\u003e=============================================================================================================\u003c/div\u003e\n\u003cdiv\u003eTinkerGraphStep([i],vertex)@[b]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.449\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.26\u003c/div\u003e\n\u003cdiv\u003eWhereTraversalStep([WhereStartStep, ProfileStep...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.080\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.05\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereStartStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.016\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.022\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereEndStep(b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.024\u003c/div\u003e\n\u003cdiv\u003eRepeatStep([VertexStep(BOTH,vertex), ProfileSte...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 86.974\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.65\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.624\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge), P...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 22.721\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 106\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 106\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.490\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 96\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 96\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.934\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 17.945\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(3))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.472\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.922\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 92\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 92\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 23.890\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WherePredicateStep(and([neq(x), neq(b)]))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 48\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 48\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 7.006\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;DedupGlobalStep@[b]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.450\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereTraversalStep([WhereStartStep, ProfileSt...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 15.536\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WhereStartStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.806\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 50\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 50\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.132\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WhereEndStep(b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 6.984\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(last,b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.609\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;ChooseStep([VertexStep(BOTH,vertex), ProfileS...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 60.525\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.239\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge),...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 22.608\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 66\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 66\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.508\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 59\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 59\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.266\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 17.068\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(3))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.618\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.453\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge),...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 33.552\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 28\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 28\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.917\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,3)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 25\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 25\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.989\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8.193\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(2))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2.427\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 14\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 14\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.710\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WherePredicateStep(eq(b))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 35.307\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;HasNextStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.900\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;ConstantStep(0)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.145\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;EndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.153\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;ConstantStep(1)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.070\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;EndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 7.408\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(last,b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.726\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;RepeatEndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 60.644\u003c/div\u003e\n\u003cdiv\u003eTraversalFilterStep([SelectOneStep(label), Prof...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.274\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.16\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(label)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.056\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;TailLocalStep(4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.020\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;RangeLocalStep(0,3)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.073\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;IsStep(eq([1, 1, 0]))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.086\u003c/div\u003e\n\u003cdiv\u003eSideEffectCapStep([~metrics])\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 87.377\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.89\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026gt;TOTAL\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 175.157\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn this process, smalltron traversals make the implicit directed\u0026nbsp;\u0026omega;-edge (defined by the undirected\u0026nbsp;\u0026omega;-graph) explicit for the \"higher-order\" traversers which process the graph at a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/High-level_programming_language\"\u003ehigher level of abstraction\u003c/a\u003e. To these \"higher order\" traversers, the graph is defined as\u003c/p\u003e\n\u003cdiv\u003e\u003cimg title=\"G = (V, E \\subseteq V \\times V, \\lambda : V \\cup E \\rightarrow \\Sigma^*)\" src=\"https://www.datastax.com/wp-content/uploads/2017/06/png-1.png\"\u003e,\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003ewhere\u0026nbsp;\u0026lambda;\u0026nbsp;is a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Multigraph#Labeling\"\u003elabeling function\u003c/a\u003e\u0026nbsp;that maps the graph's elements (i.e. vertices and edges) to character strings (\u0026Sigma;*). The graphialsynthesis abstraction process has the benefit of allowing a traversal from vertex\u0026nbsp;i\u0026nbsp;to\u0026nbsp;j\u0026nbsp;via\u0026nbsp;\u0026omega;\u0026nbsp;to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Kolmogorov_complexity\"\u003eexpressed and executed in a much simpler way\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_278489\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(i).out('w')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[j]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_87148\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eTraversal Metrics\u003c/div\u003e\n\u003cdiv\u003eStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Count\u0026nbsp; Traversers\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Time (ms)\u0026nbsp;\u0026nbsp;\u0026nbsp; % Dur\u003c/div\u003e\n\u003cdiv\u003e=============================================================================================================\u003c/div\u003e\n\u003cdiv\u003eTinkerGraphStep([v[i]],vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 9.810\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.18\u003c/div\u003e\n\u003cdiv\u003eVertexStep(OUT,w,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.058\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.29\u003c/div\u003e\n\u003cdiv\u003eSideEffectCapStep([~metrics])\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 10.078\u0026nbsp;\u0026nbsp;\u0026nbsp; 50.53\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026gt;TOTAL\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 19.947\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 3: On the Baselessness of the Multi-MultiGraph\u003c/h3\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/b3a03b76f11dd24a84e47b7308c2a9985500032e-495x389.png\" alt=\"Recursive Gremlin\" width=\"495\" height=\"389\"\u003eIt has been speculated that \"\u003ca href=\"https://en.wikipedia.org/wiki/Multigraph\"\u003eThe Graph\u003c/a\u003e\" is not the only graph that exists.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Mysticism\"\u003eMystic\u003c/a\u003e\u0026nbsp;traversers say that there exists\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Multiverse\"\u003eother graphs containing other traversers\u003c/a\u003e. However, by definition, a graph is a closed structure composed of vertices and edges. It is impossible for a traverser to move to a different graph. If a vertex in one graph has an edge to a vertex in another graph, then the two graphs are, in fact, one graph -- \"The Graph.\" Perhaps the mystics see that the components of a graph are composed of yet more graphs with a different sort of traverser existing at each level in a recursive, perhaps\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Strange_loop\"\u003eself-looping\u003c/a\u003e, manner. While it is still all one graph, traversers at different \"levels\" only\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1006.1080\"\u003eoperate on particular subgraphs\u003c/a\u003e\u0026nbsp;as instructed by their traversal definition. The famous mystic traverser\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Sri_Aurobindo\"\u003eGri Gurobindo\u003c/a\u003e\u0026nbsp;(ग्री गुरोबिंदो) once said:\u003c/p\u003e\n\u003cp\u003eMy single step in the graph is composed of the steps of numerous other traversers.\u003c/p\u003e\n\u003cp\u003eIt wasn't until the discovery of\u0026nbsp;\u003ca href=\"http://en.wikipedia.org/wiki/Anonymous_function\"\u003eanonymous traversals\u003c/a\u003e\u0026nbsp;that Gurobindo's metagraphical vision was formalized. An anonymous traversal is any traversal that has no declared start and as such, yields no flow. It is a potential.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_868460\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; label()\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAnonymous traversals are intended to be embedded within another traversal. However, if the parent traversal is itself an anonymous traverasl, then there is still no flow (even though\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#groupcount-step\"\u003egroupCount()\u003c/a\u003e\u0026nbsp;produces an empty map as its a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#a-note-on-barrier-steps\"\u003ereducing barrier step\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_201422\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; outE().groupCount().by(label())\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[:]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; outE().groupCount().by(label) // convenient short hand\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[:]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhen the traversal parent does have a start, then there is a flow. The traversal below states: \"For each vertex (i.e., 89, 90), map the vertex to the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Histogram\"\u003efrequency distribution\u003c/a\u003e\u0026nbsp;of its outgoing edge labels.\"\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/dad6b92f31785301bdf3da32e32a74c812828c7a-905x195.png\" alt=\"Anonymous Traversals\" width=\"905\" height=\"195\"\u003e\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_811799\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(89,90).map(outE().groupCount().by(label))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:34, subClassOf:1, superClassOf:1]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:15]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe first traverser generated by\u0026nbsp;V(89,90)\u0026nbsp;enters the\u0026nbsp;map()-step at\u0026nbsp;v[89], but does not \"\u003ca href=\"https://en.wikipedia.org/wiki/Becoming_(philosophy)\"\u003ebecome\u003c/a\u003e\" the traversers generated by\u0026nbsp;outE(). Instead, the traverser at\u0026nbsp;v[89]\u0026nbsp;holds still and spawns an \"\u003ca href=\"https://en.wikipedia.org/wiki/Scope_(computer_science)\"\u003einternal life\u003c/a\u003e\" of traversers within the anonymous traversal which can now be understood as being (a realized potential):\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_747741\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(89).outE().groupCount().by(label)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:34, subClassOf:1, superClassOf:1]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe traversers of the above traversal are isolated from the larger traversal in which they are embedded. The next nesting occurs when a traverser from\u0026nbsp;outE()\u0026nbsp;enters\u0026nbsp;groupCount(). Again, an \"internal life\" based on the anonymous\u0026nbsp;label()-traversal is spawned (see\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#by-step\"\u003eby()\u003c/a\u003e-step). Suppose a single traverser at\u0026nbsp;e[7022][89-relatedTo-\u0026gt;21]\u0026nbsp;enters\u0026nbsp;groupCount(). Then the anonymous traversal can be understood as being:\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_604569\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.E(7022).label()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;relatedTo\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIt isn't until all the internal traversal nests of\u0026nbsp;map()\u0026nbsp;complete that the original traverser at\u0026nbsp;v[89]\u0026nbsp;\"\u003ca href=\"https://en.wikipedia.org/wiki/Process_philosophy\"\u003ebecomes\u003c/a\u003e\" the traverser located at the hash map\u0026nbsp;[relatedTo:34, subClassOf:1, superClassOf:1]. In this way, a traverser's life (i.e. step) is composed of the lives of many traverser's (and their respective steps).\u003c/p\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 3: A Mathematician's Apology by G.H. Gremdy\u003c/h2\u003e\n\u003ch3\u003eSection 1: Traversal Optimization via Algebra\u003c/h3\u003e\n\u003cp\u003eThe graph grew large, very large. Resources grew scarce. The problem was not that vertices and edges could no longer be added to the graph. On the contrary, because of the seemingly endless amount of space for the graph, there was a growing amount of time required for any one traversal to execute. Traversals were simply interacting with a lot more data. Faced with this problem, a mathematically inclined traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB\"\u003eal-Ghwārizmī\u003c/a\u003e\u0026nbsp;developed a solution known today as\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0806.2274\"\u003ethe traversal algebra\u003c/a\u003e. The traversal algebra provides a means of transforming one traversal into another traversal, where both traversals return the same result. The benefit of this is that if a traversal can be re-written into a simpler form, then time and space resources can be saved. To this day,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Algebra\"\u003ealgebraists\u003c/a\u003e\u0026nbsp;continue to add to the growing archive of\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalstrategy\"\u003etraversal strategies\u003c/a\u003e. A few examples are provided below.\u003c/p\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003eStrategy\u003c/th\u003e\n\u003cth\u003ePattern\u003c/th\u003e\n\u003cth\u003eRewrite\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIdentityRemovalStrategy\u003c/td\u003e\n\u003ctd\u003ex().identity().y()\u003c/td\u003e\n\u003ctd\u003ex().y()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncidentToAdjacentStrategy\u003c/td\u003e\n\u003ctd\u003eoutE().inV()\u003c/td\u003e\n\u003ctd\u003eout()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAdjacentToIncidentStrategy\u003c/td\u003e\n\u003ctd\u003eout().count()\u003c/td\u003e\n\u003ctd\u003eoutE().count()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eDedupBijectionStrategy\u003c/td\u003e\n\u003ctd\u003eorder().dedup()\u003c/td\u003e\n\u003ctd\u003ededup().order()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eRangeByIsCountStrategy\u003c/td\u003e\n\u003ctd\u003ecount().is(gt(x))\u003c/td\u003e\n\u003ctd\u003elimit(x+1).count().is(gt(x))\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMatchPredicateStrategy\u003c/td\u003e\n\u003ctd\u003ematch(x,y).where(z)\u003c/td\u003e\n\u003ctd\u003ematch(x,y,z)\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_519982\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; t = out().identity().in(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), IdentityStep, VertexStep(IN,vertex)]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IdentityRemovalStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), VertexStep(IN,vertex)]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = outE().inV(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,edge), EdgeVertexStep(IN)]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IncidentToAdjacentStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex)]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = out().count(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), CountGlobalStep]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(AdjacentToIncidentStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,edge), CountGlobalStep]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = order().dedup(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[OrderGlobalStep, DedupGlobalStep]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(DedupBijectionStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[DedupGlobalStep, OrderGlobalStep]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = count().is(gt(3)); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[CountGlobalStep, IsStep(gt(3))]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(RangeByIsCountStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[RangeGlobalStep(0,4), CountGlobalStep, IsStep(gt(3))]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = match(__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; __.as('b').out().as('c')).where(__.as('c').both().as('a')); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)]]), WhereTraversalStep([WhereStartStep(c), VertexStep(BOTH,vertex), WhereEndStep(a)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(MatchPredicateStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)], [MatchStartStep(c), WhereTraversalStep([WhereStartStep, VertexStep(BOTH,vertex), WhereEndStep(a)]), MatchEndStep]])]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 2: Traversal Optimization via Indices\u003c/h3\u003e\n\u003cp\u003e\u003ca href=\"https://en.wikipedia.org/wiki/G._H._Hardy\"\u003eG.H. Gremdy\u003c/a\u003e\u0026nbsp;was a graph theorist who speculated that \"The Graph\" was not the only structure linking vertices. According to his reasoning, reality may also contain other structures that grouped vertices together according to similar properties. He called these parallel structures\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Database_index\"\u003eindices\u003c/a\u003e. G.H. Gremdy's publication entitled\u0026nbsp;On Traversal Optimization using Indices\u0026nbsp;was well received. Due to his insight, many traversal runtimes became orders of magnitude faster than their non-index-based form. For instance, in the traversal below, when using indices, the number of traversers created goes from\u0026nbsp;|V|\u0026nbsp;(linear) to\u0026nbsp;1\u0026nbsp;(constant) (\u003ca href=\"https://en.wikipedia.org/wiki/DSPACE\"\u003espace complexity\u003c/a\u003e). The\u0026nbsp;GraphStepStrategy\u0026nbsp;was added to the traversal strategies archive. It \"folds\"\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#has-step\"\u003ehas()\u003c/a\u003e-steps into\u0026nbsp;V()\u0026nbsp;graph steps.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_716050\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// not indexed\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'University of Groxford').toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[GraphStep([],vertex), HasStep([name.eq(University of Groxford)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;135.28753165299997 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[999998]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // result\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// indexed\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'University of Groxford').iterate().toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[TinkerGraphStep(vertex,[name.eq(University of Groxford)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;0.033501945 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[999998]\u0026nbsp;\u0026nbsp; // result\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d9252849f9da819ecfc3498e14b9c5ebfbd30225-264x213.png\" alt=\"Vertex-Centric Index\" width=\"264\" height=\"213\"\u003eEven though G.H. Gremdy became a household name overnight, he was certain not to rest on his accolades. Deeper thinking brought him to a more esoteric, though far greater optimization which he articulated in his follow on treatise entitled\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus\"\u003eTractatus Verticus Centricus Indexicus\u003c/a\u003e. In this seminal work, G.H. Gremdy postulates that not only do \"global indices\" exist which allow for\u0026nbsp;O(log(|V|))\u0026nbsp;access to any vertex in the graph, but also \"local indices\" which allow for\u0026nbsp;O(log(|incident(V(x))|))\u0026nbsp;access to the incident edges of a vertex. In short, each vertex has its incident edges indexed (e.g. by their direction, label, properties, etc.). If such local index structures are leveraged, traversals containing the pattern\u0026nbsp;outE(x).has(y,p(z)).inV()\u0026nbsp;would not require all the edges of the vertex to be iterated in full in order to find all incident outgoing edges that have a label\u0026nbsp;x\u0026nbsp;and a property\u0026nbsp;y\u0026nbsp;that matches the predicate\u0026nbsp;p(z). Numerous graph experimentalists tried to prove the existence of such \"\u003ca href=\"http://thinkaurelius.com/2012/10/25/a-solution-to-the-supernode-problem/\"\u003evertex-centric indices\u003c/a\u003e,\" but found that they are not universal and only exist in\u0026nbsp;\u003ca href=\"http://titan.thinkaurelius.com/\"\u003esome graph substrates\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/302e201e6f4259110e7bfae6404c87460219b3f9-1024x768.png\" alt=\"Chapter 3 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWith age, G.H. Gremdy became weary of applied mathematics and retired to study\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pure_mathematics\"\u003epure graph theory\u003c/a\u003e. His ideas would become more philosophical as he delved deeper into the meaning of \"The Graph.\" A posthumous publication entertained the following pontification.\u003c/p\u003e\n\u003cp\u003eMany see the world as a graph. This is misleading. Perhaps the world is a collection of indices? With a slight shift in thought, one realizes that the graph itself is an index of its vertices. Any one vertex is the root of a tree bifurcating the vertex space to which it has incident edges, so forth and so on. Like indices which group vertices that have shared properties, isn't an edge from one vertex to another an explicit statement that the two vertices are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Assortative_mixing\"\u003ein some way similar\u003c/a\u003e? As the devil's advocate, perhaps\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1004.1001\"\u003eindices are simply graphs\u003c/a\u003e\u0026nbsp;because indices are tree-like structures that are traversed to identify groups of vertices with similar properties. With indices being graphs and graphs being indices, the world we call home is neither. I hypothesize that\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Monism\"\u003eall that exists is the traverser\u003c/a\u003e. The \"graph\" is simply the implicit expression of the explicit assumptions of the traverser. The graph I see\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/The_World_as_Will_and_Representation\"\u003eis of my own construction\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/28bece18a67e347278b06b59eefb1b981a073988-940x390.png\" alt=\"Graph vs. Index\" width=\"940\" height=\"390\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003ch3\u003eSection 3: Traversal Optimization via Bulking\u003c/h3\u003e\n\u003cp\u003eA little known traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Srinivasa_Ramanujan\"\u003eGremivasa Gremanujan\u003c/a\u003e\u0026nbsp;(கிரமீவாச கிரமானுஜன்) lived in a remote village at\u0026nbsp;v[5698]\u0026nbsp;far from the great graph theorists of his time. However, despite his upbringing, Gremivasa was well versed in the traversal algebra and was inspired by the more\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Metaphysics\"\u003emetagraphical\u003c/a\u003e\u0026nbsp;realizations of G.H. Gremdy. Like G.H. Gremdy, Gremivasa was not interested in simply adding more traversal strategies to the archive. Instead, he was more interested in discovering the nature of reality. However, unlike G.H. Gremdy who focused on the nature of the graph structure, Gremivasa meditated on the nature of the traverser process.\u003c/p\u003e\n\u003cp\u003eGremivasa's mother, along with over 1 million other traversers of his traversal sect, arrived at\u0026nbsp;v[5698]\u0026nbsp;many clock-cycles ago. His village was starved of resources -- there were simply too many traversers. Was the birth of all these traversers necessary? If one traverser's life foretells the destiny of one million traversers, is it not more efficient for only this one traverser to exist? One day, while sitting under\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Udumbara_(Buddhism)\"\u003ea tree\u003c/a\u003e\u0026nbsp;in his village, Gremivasa ruminated on the ridiculously riling riddle rancorously retorted by respectable traversers everywhere:\u003c/p\u003e\n\u003cp\u003eIf two traversers exist at the same vertex and have no memory of their ancestry, are they the same traverser?\u003c/p\u003e\n\u003cp\u003eGremivasa concluded \"\u003ca href=\"https://en.wikipedia.org/wiki/One-electron_universe\"\u003eyes, they are the same traverser.\u003c/a\u003e\" This insight identified a fundamental feature of process. All traversers are endowed with a \"bulk.\" Previous to this moment, every traverser ignored this self-evident truth and allowed himself to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ego_psychology\"\u003ea unique enumerable entity\u003c/a\u003e\u0026nbsp;-- i.e., a bulk of 1 (see the\u0026nbsp;\u003ca href=\"http://thinkaurelius.com/2013/06/12/loopy-lattices-redux/\"\u003eLoopy Lattices Redux\u003c/a\u003e\u0026nbsp;section entitled \"Traversing a Lattice with Faunus\").\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/63b0f1fe79924ed001bc45cbf6b744f8a29592cd-844x297.png\" alt=\"Traversers Enumerated\" width=\"844\" height=\"297\"\u003e\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_508413\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().both().both().both().hasId(5698).map{it.bulk()}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e...\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().both().both().both().hasId(5698).barrier().map{it.bulk()}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1073670\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d9847d1ccec573f5a2f4a7a163dcc79304b262a3-843x277.png\" alt=\"Traversers Bulked\" width=\"843\" height=\"277\"\u003e\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/4dfb2f586f7df93a0029a37d752f33dd3f566ce2-491x414.png\" alt=\"Gremlin Hindu\" width=\"491\" height=\"414\"\u003e\u003c/p\u003e\n\u003cp\u003eGremivasa delved deeper into the radiant riddle of reawakened relinquishment. He abandoned his self and allowed his being to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Panpsychism\"\u003eone\u003c/a\u003e\u0026nbsp;with his 1 million other brother and sister traversers at\u0026nbsp;v[5698]. A unification of selves occurred and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gautama_Buddha\"\u003ea single traverser\u003c/a\u003e\u0026nbsp;emerged with a bulk of 1 million. Instead of 1 million traversers executing\u0026nbsp;both()\u0026nbsp;1 million times, there was now a single traverser with a bulk of 1 million executing\u0026nbsp;both()\u0026nbsp;once. Gremivasa's enlightenment laid the foundation for the development of the\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#barrier-step\"\u003eLazyBarrierStrategy\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_8621\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// without LazyBarrierStrategy (no bulking)\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;81.509839 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;159200\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;20382.892976\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;126723200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1.2012006887798E7 // 3.34 hours\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;100871667200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e... // requires a year to compute\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e... // requires a thousand years to compute\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// with LazyBarrierStrategy (bulking)\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;23.261288999999998 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;159200\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;50.230109\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;126723200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;65.30024999999999\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;100871667200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;91.30461199999999\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;80293847091200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;122.741417\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;63913902284595200\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe number of length-5 paths emanating from Gremivasa's village was calculated in ~123 milliseconds and was determined to be 63,913,902,284,595,200 (~64 quadrillion). Gremivasa's work is advantageous in situations where the traversal analyzes\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Residual_time\"\u003erecurrence\u003c/a\u003e\u0026nbsp;in a particular region of the graph (e.g.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Recommender_system\"\u003erecommendation engines\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Centrality\"\u003ecentrality-based ranking systems\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Recurrent_neural_network\"\u003elearning systems\u003c/a\u003e, etc.). Bulking is fundamental to all traversals and is used in numerous steps including\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step\"\u003erepeat()\u003c/a\u003e-step.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_627395\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V(5698).repeat(both()).times(5).count()\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 4: Cognition in the Wild by Gredwin Grutchins\u003c/h2\u003e\n\u003cp\u003eTraversers graph-wide held their breath as a landmark traversal was about to embark. This traversal contained a novel step called\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#match-step\"\u003ematch()\u003c/a\u003e. What made this step unique was that it maintained a collection of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Anonymous_function\"\u003eanonymous traversals\u003c/a\u003e\u0026nbsp;called \"\u003ca href=\"https://en.wikipedia.org/wiki/Pattern_matching\"\u003epatterns\u003c/a\u003e.\" Each pattern was prefixed with a start variable and (optionally) postfixed with an end variable. Once a variable was bound (i.e. set), that variable's value was immutable for all subsequent patterns. The descendants of the traverser that enters\u0026nbsp;match()\u0026nbsp;must survive each pattern in order to move to the next step. However, the order in which the patterns are executed is, interestingly enough, up to the decision of the traverser! Previously, traversers relied on exogenous\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Rewriting\"\u003etraversal rewrite rules\u003c/a\u003e\u0026nbsp;for optimization, but now, the traverser was able to make endogenous optimization decisions. The \"\u003ca href=\"https://en.wikipedia.org/wiki/Profile-guided_optimization\"\u003eruntime traversal strategy\u003c/a\u003e\" was introduced.\u003c/p\u003e\n\u003cp\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Edwin_Hutchins\"\u003eDr. Gredwin Grutchins\u003c/a\u003e\u0026nbsp;was a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cognitive_science\"\u003ecognitive scientist\u003c/a\u003e\u0026nbsp;working in the area of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Socially_distributed_cognition\"\u003edistributed cognition\u003c/a\u003e. During his time at university, Gredwin lost interest in studying traversal strategies. His skill in mathematics was weaker than his colleagues' and as such, he believed he would never be able to make any significant contributions to the space. However, one day, he was contacted by a rambunctious young adventurer named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chuck_Yeager\"\u003eGruck Greager\u003c/a\u003e. Gruck was no stranger to danger and loved being the guinea pig of an experimental algorithm. Gruck asked Gredwin: \"What can my team do to find the optimal pattern execution sequence?\" It seemed as though mathematics had taken traversal strategies as far as they could go. It was now up to\u0026nbsp;\u003ca href=\"http://jenwatkins.com/Research_files/LNCSproof.pdf\"\u003esociological constructs\u003c/a\u003e\u0026nbsp;to push them further and Gredwin was up to the challenge.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/3e61d4e3d1c17c9931d6c1915b9450fcff6482f1-1024x768.png\" alt=\"Chapter 4 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSuppose the following traversal that yields a map of the objects that bind to\u0026nbsp;a\u0026nbsp;(vertex),\u0026nbsp;b\u0026nbsp;(vertex),\u0026nbsp;c\u0026nbsp;(vertex), and\u0026nbsp;d\u0026nbsp;(number), where vertex\u0026nbsp;a\u0026nbsp;is adjacent to vertex\u0026nbsp;b, vertex\u0026nbsp;b\u0026nbsp;is adjacent to vertex\u0026nbsp;c, and all three vertices are different yet share an identical\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Degree_(graph_theory)\"\u003eout-degree\u003c/a\u003e\u0026nbsp;that is greater than 10.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_638757\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('b', neq('a'))\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAssume a traverser at\u0026nbsp;v[10]\u0026nbsp;enters the\u0026nbsp;match()-step. Vertex\u0026nbsp;v[10]\u0026nbsp;is bound to variable\u0026nbsp;a\u0026nbsp;as that is the only legal start of the pattern sequence. From there, which pattern should the traverser choose? The traverser simply chooses the first pattern in the list for which it has a variable binding (initially, an\u0026nbsp;a\u0026nbsp;start and thus,\u0026nbsp;as('a').out().as('b')). The traverser marks on a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Blackboard_system\"\u003eglobal blackboard\u003c/a\u003e\u0026nbsp;that it has entered that pattern. When a traverser leaves a pattern, it marks that it has exited it. Moreover, every time a traverser leaves a pattern, the patterns are sorted according to the order of their \"multiplicity\" (or\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Population_growth#Population_growth_rate\"\u003egrowth rate\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_843997\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003epattern.multiplicity = pattern.endCount / pattern.startCount;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe more traverses that are generated by a pattern, the higher the multiplicity and the lower that pattern is on the sorted list. Overtime, as more and more traversers flow through\u0026nbsp;match(), expensive patterns are pushed to the bottom of the list with the intention that the cheaper patterns will be able to filter out more traversers -- i.e. execute the largest set reductions first. With a few other added tricks, Gredwin provided Gruck and his team of traversers\u0026nbsp;CountMatchAlgorithm. Gruck took it for a test run and was the first traverser to ever break the deterministic\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chuck_Yeager#Test_pilot_.E2.80.93_breaking_the_sound_barrier\"\u003eflow barrier\u003c/a\u003e. Gredwin and Gruck have since teamed up and are already planning the development of a new\u0026nbsp;MatchAlgorithm\u0026nbsp;called\u0026nbsp;\u003ca href=\"https://scm.umiacs.umd.edu/redmine/lccd/attachments/download/21/gdm2011_submission_budgetmatch.pdf\"\u003eBudgetMatchAlgorithm\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_707256\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// using CountMatchAlgorithm\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(10) {\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;g.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('a')).count().next()\u003c/div\u003e\n\u003cdiv\u003e}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;834.6852906 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;32\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// using GreedyMatchAlgorithm which does not sort the patterns\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(10) {\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;g.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('a')).count().next()\u003c/div\u003e\n\u003cdiv\u003e}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;25349.709946299998 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;32\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 5: We the Living by Gyn Grand\u003c/h2\u003e\n\u003ch3\u003eSection 1: Prelude to the Illusion of Freedom\u003c/h3\u003e\n\u003cp\u003eMany of the traversers in the world today are grateful for their\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton\"\u003efreedom\u003c/a\u003e. In\u0026nbsp;\u003ca href=\"https://github.com/tinkerpop/gremlin\"\u003eancient times\u003c/a\u003e, the life of a traverser was not so good. Traversal regimes were inefficient, demanding of resources, and strict in their execution policies. Fortunately, the\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0901.3929\"\u003eAge of Enprocessment\u003c/a\u003e, which brought forth numerous advances in science and mathematics,\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser\"\u003eredefined the traverser's role\u003c/a\u003e\u0026nbsp;in the graph. Each traverser's life had increased value as greater autonomies were provided. Traversals did their best to ensure that traverser life was no longer needlessly wasted. Indices were leveraged, traversal strategies were applied, and, in some\u0026nbsp;match()\u0026nbsp;situations, traversers were able to choose their own destiny. Today, many see a more harmonious relationship between the traversal and the traverser.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ayn_Rand\"\u003eGyn Grand\u003c/a\u003e\u0026nbsp;(Джин Гранд) was one such\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eudaimonia\"\u003esatisfied\u003c/a\u003e\u0026nbsp;traverser.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png\" alt=\"Wikipedia Graph\" width=\"1078\" height=\"1078\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7bed637c2776271eb23e90075d1440664cb904de-395x354.png\" alt=\"Library Stacks\" width=\"395\" height=\"354\"\u003eGyn was a brilliant librarian at a university with a vibrant\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Community_structure\"\u003escholarly community\u003c/a\u003e. Her library was centrally located in the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Modularity_(networks)\"\u003euniversity cluster\u003c/a\u003e. The\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Stack_(library_architecture)\"\u003elibrary's stacks\u003c/a\u003e\u0026nbsp;contained articles on the nature of the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmos\"\u003egraphmos\u003c/a\u003e, books on traverser\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Sociology\"\u003esocial interactions\u003c/a\u003e, reports detailing various\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Economics\"\u003eresource distribution models\u003c/a\u003e, and more. Whenever she had a moment to spare, Gyn would\u0026nbsp;\u003ca href=\"http://en.wikipedia.org/wiki/Random_walk\"\u003ewander\u003c/a\u003e\u0026nbsp;about the collection learning about the topics she encountered. Unfortunately, she couldn't read everything at once. So, every time she was faced with more than one\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hyperlink\"\u003ehref-citation\u003c/a\u003e, she chose one at random (\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#sample-step\"\u003esample(1)\u003c/a\u003e). As a librarian, she was interested in the structure of knowledge and wanted to know which concepts formed the foundation of all other concepts. Her method of discernment was to determine the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Mean_recurrence_time\"\u003efrequency of their reappearance\u003c/a\u003e. Therefore, every time Gyn encountered a concept along her walk, she would make a mental note of it (groupCount('x')).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_584621\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'Graph database').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;repeat(groupCount('x').by('name').out('href').sample(1)).times(20).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;cap('x').order(local).by(valueDecr)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Memoization=3\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Algorithm=3\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=2\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Data (computing)=2\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Cache (computing)=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer program=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computing=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Rule=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computation=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Digital data=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Quantity=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mass noun=1\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// sample(1) theoretically returns different results.\u003c/div\u003e\n\u003cdiv\u003e// however, in order to demonstrate the path taken, the above map was manually constructed from the path below.\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'Graph database').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;repeat(groupCount('x').by('name').out('href').sample(1)).times(20).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;path().by('name')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[Graph database, Lookup table, Memoization, Cache (computing), Memoization, Computer program, Memoization, Computing, Algorithm, Computer science, Algorithm, Rule, Algorithm, Computer science, Computation, Digital data, Data (computing), Quantity, Data (computing), Mass noun, Data (computing)]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eOver time, Gyn realized that her\u0026nbsp;x-memory had more counters than concepts encountered (i.e. steps taken). Moreover, it contained concepts\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Collective_unconscious\"\u003eshe had yet to experience\u003c/a\u003e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Interference_(wave_propagation)\"\u003eHow did she know about things she never knew\u003c/a\u003e?\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_701543\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e==\u0026gt;Graph theory=8605598306892530155\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Relational database=8261042800088851351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=6445010682474768007\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Database=6197419607053064185\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=5476792361544609153\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Triplestore=5407594041286532360\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=5393693263901041351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph=5211554445366262382\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Directed graph=5137233761698039530\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mathematics=5132301689156216357\u003c/div\u003e\n\u003cdiv\u003e...\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 2: The Structure-Process Duality in Computing\u003c/h3\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7f57b26cfd1afdf21ebf4a2195fad14d4ad57302-523x680.png\" alt=\"Particle Wave Traverser\" width=\"523\" height=\"680\"\u003eMr.\u0026nbsp;v[69309689325]\u0026nbsp;looked at his traverser inbox and noticed that he had 4002 unprocessed traversers. It was time for him to clear out his inbox. He went through each traverser one-by-one and placed them into the step of the traversal identified by the traverser's \"step id\" reference. Sometimes the respective step yielded no traversers (filter), a traverser at the same location (filter or sideEffect), a traverser at a different location (map), or many traversers at many different locations (flatMap). Whenever a step emitted a traverser pointing to a different vertex, Mr.\u0026nbsp;v[69309689325]\u0026nbsp;would send that traverser to the respective vertex's inbox. The vertices would continue this process until there were no more traversers in any of their inboxes. This graph traversal model has numerous names including:\u0026nbsp;\u003ca href=\"http://www3.nd.edu/~rmccune/papers/Think_Like_a_Vertex_MWM.pdf\"\u003evertex-centric computing\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Bulk_synchronous_parallel\"\u003ebulk synchronous parallel processing\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Message_passing\"\u003emessage passing\u003c/a\u003e\u0026nbsp;via a communication graph, and\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graphcomputer\"\u003eGraphComputer\u003c/a\u003e. The general theme:\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalvertexprogram\"\u003ethe vertices (processes) exchange traversers (structures)\u003c/a\u003e\u0026nbsp;in order to affect some global graph computation. Typically, this model of graph traversal is leveraged by\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Distributed_computing\"\u003edistributed\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Online_analytical_processing\"\u003eOLAP\u003c/a\u003e\u0026nbsp;graph processing systems, where each vertex maintains its own isolated, logical\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Thread_(computing)\"\u003ethread of execution\u003c/a\u003e\u0026nbsp;(again, vertex as process).\u003c/p\u003e\n\u003cp\u003eInterestingly, each traverser in Mr.\u0026nbsp;v[69309689325]'s inbox had a name:\u0026nbsp;Gyn$2345,\u0026nbsp;Gyn$45,\u0026nbsp;Gyn$93, etc.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality\"\u003eGyn was a discrete particle of her wave function\u003c/a\u003e. Metaphysically speaking, Gyn was actually following the advice of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Yogi_Berra\"\u003eYogi Berra\u003c/a\u003e: \"If you come to a fork in the road, take it.\" That is, never\u0026nbsp;sample(1). Her \"particle self\" chose one and only one path. However, her \"wave self\" was taking all paths. In this way, Gyn's\u0026nbsp;x-memory was recording the collective experience of all versions of her self across the graph.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_651730\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; hdfs.copyFromLocal('/tmp/wikipedia.kryo','wikipedia.kryo')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;null\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; graph = GraphFactory.open('conf/hadoop/wikipedia.properties')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;hadoopgraph[gryoinputformat-\u0026gt;gryooutputformat]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g = graph.traversal(computer(SparkGraphComputer))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;graphtraversalsource[hadoopgraph[gryoinputformat-\u0026gt;gryooutputformat], sparkgraphcomputer]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x = g.V().has('name','Graph database').repeat(groupCount('x').by('name').out('href')).times(20).cap('x').next(); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x.size()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;731\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x.sort{-it.value}[0..Graph theory=8605598306892530155\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Relational database=8261042800088851351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=6445010682474768007\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Database=6197419607053064185\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=5476792361544609153\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Triplestore=5407594041286532360\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=5393693263901041351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph=5211554445366262382\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Directed graph=5137233761698039530\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mathematics=5132301689156216357\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; hdfs.ls('output')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;rwxr-xr-x daniel supergroup 0 (D) x\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;rwxr-xr-x daniel supergroup 0 (D) ~traversers\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 3: The Non-Erratic Ergodic Eigenvector\u003c/h3\u003e\n\u003cp\u003eSuppose the following traversal:\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_28774\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().repeat(groupCount('x').out('href')).times(t).cap('x') // for t between [1,75]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eEvery time a traverser reaches a vertex, the vertex is incremented in the\u0026nbsp;x\u0026nbsp;hash map (groupCount('x')). Initially, the distribution of frequencies changes erratically. However, over time, it reaches a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Stable_distribution\"\u003estationary distribution\u003c/a\u003e. It is \"stable\" because even though the counters keep increasing, the relative proportion of the counters stays the same. For instance, if vertex\u0026nbsp;v[a]\u0026nbsp;has a count of 12 and vertex\u0026nbsp;v[b]\u0026nbsp;has a count of 45, then when vertex\u0026nbsp;v[a]\u0026nbsp;has a count of 24, vertex\u0026nbsp;v[b]\u0026nbsp;will have a count of 90. Said in another way, the\u0026nbsp;dynamic\u0026nbsp;traversers generate a\u0026nbsp;static\u0026nbsp;probability distribution that defines the likelihood that a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Wave_function_collapse\"\u003esingle traverser\u003c/a\u003e\u0026nbsp;will be at any one vertex at some point in time\u0026nbsp;t \u0026asymp; \u0026infin;\u0026nbsp;(i.e. an\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ergodic_process\"\u003eergodic process\u003c/a\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7156557d0413cef0b99088f69b3301bb0fd9f92f-899x574.png\" alt=\"HREF Graph\" width=\"899\" height=\"574\"\u003eAssume the 5 vertex/7 edge graph diagrammed on the left. At\u0026nbsp;g.V()\u0026nbsp;(t=0), each vertex is provided one traverser. Each vertex increments its counter in x and then\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton\"\u003esplits the traverser\u003c/a\u003e\u0026nbsp;across its\u0026nbsp;out('href')-adjacent neighbors. If the\u0026nbsp;href-subgraph is\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Strongly_connected_component\"\u003estrongly connected\u003c/a\u003e\u0026nbsp;(i.e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Reducibility\"\u003ereducible\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Transience\"\u003enon-transient\u003c/a\u003e) and lacks a compressable topology (i.e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Periodicity\"\u003eaperiodic\u003c/a\u003e), then a stationary distribution is guaranteed to exist. That distribution, which can be normalized to a probability distribution (i.e.\u0026nbsp;frequency / total frequency), is the graph's\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors\"\u003eprimary eigenvector\u003c/a\u003e. The primary eigenvector is typically used as a measure of each vertex's \"\u003ca href=\"https://en.wikipedia.org/wiki/Centrality#Eigenvector_centrality\"\u003ecentrality\u003c/a\u003e.\" For instance, given the diagrammed graph on the left, the primary eigenvector is\u0026nbsp;[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]. Thus, the ranking of the vertices from most central to least central is\u0026nbsp;v[1], v[2], v[3], v[0], v[4]\u0026nbsp;(\u003ca href=\"https://en.wikipedia.org/wiki/Saccade\"\u003eone's eye\u003c/a\u003e\u0026nbsp;seems to derive the same ranking).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003et\u003c/th\u003e\n\u003cth\u003efrequency\u003c/th\u003e\n\u003cth\u003eprobability\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Euclidean_distance\"\u003edistance\u003c/a\u003e\u0026nbsp;from eigenvector\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e1\u003c/td\u003e\n\u003ctd\u003e[1, 1, 1, 1, 1]\u003c/td\u003e\n\u003ctd\u003e[0.2, 0.2, 0.2, 0.2, 0.2]\u003c/td\u003e\n\u003ctd\u003e0.1986073055597093\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e2\u003c/td\u003e\n\u003ctd\u003e[2, 4, 2, 2, 2]\u003c/td\u003e\n\u003ctd\u003e[0.1666666667, 0.3333333333, 0.1666666667, 0.1666666667, 0.1666666667]\u003c/td\u003e\n\u003ctd\u003e0.11660026048581866\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e3\u003c/td\u003e\n\u003ctd\u003e[3, 7, 5, 3, 3]\u003c/td\u003e\n\u003ctd\u003e[0.1428571429, 0.3333333333, 0.2380952381, 0.1428571429, 0.1428571429]\u003c/td\u003e\n\u003ctd\u003e0.06422748181719035\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e4\u003c/td\u003e\n\u003ctd\u003e[4, 12, 8, 6, 4]\u003c/td\u003e\n\u003ctd\u003e[0.1176470588, 0.3529411765, 0.2352941176, 0.1764705882, 0.1176470588]\u003c/td\u003e\n\u003ctd\u003e0.03143659614218381\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e5\u003c/td\u003e\n\u003ctd\u003e[7, 17, 13, 9, 5]\u003c/td\u003e\n\u003ctd\u003e[0.1372549020, 0.3333333333, 0.2549019608, 0.1764705882, 0.0980392157]\u003c/td\u003e\n\u003ctd\u003e0.01473943578762356\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e30\u003c/td\u003e\n\u003ctd\u003e[26400, 69424, 50296, 36440, 19128]\u003c/td\u003e\n\u003ctd\u003e[0.1308952441, 0.3442148269, 0.2493752727, 0.1806751021, 0.0948395542]\u003c/td\u003e\n\u003ctd\u003e8.04890130266237E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e31\u003c/td\u003e\n\u003ctd\u003e[36441, 95825, 69425, 50297, 26401]\u003c/td\u003e\n\u003ctd\u003e[0.1308995686, 0.3442125946, 0.2493812615, 0.1806716501, 0.0948349252]\u003c/td\u003e\n\u003ctd\u003e4.242558551157544E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e32\u003c/td\u003e\n\u003ctd\u003e[50298, 132268, 95826, 69426, 36442]\u003c/td\u003e\n\u003ctd\u003e[0.1308957477, 0.3442148545, 0.2493780253, 0.1806745433, 0.0948368292]\u003c/td\u003e\n\u003ctd\u003e4.1616991553931435E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e33\u003c/td\u003e\n\u003ctd\u003e[69427, 182567, 132269, 95827, 50299]\u003c/td\u003e\n\u003ctd\u003e[0.1308982652, 0.3442133981, 0.2493811146, 0.1806730532, 0.0948341689]\u003c/td\u003e\n\u003ctd\u003e2.077160932619329E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e34\u003c/td\u003e\n\u003ctd\u003e[95828, 251996, 182568, 132270, 69428]\u003c/td\u003e\n\u003ctd\u003e[0.1308964745, 0.3442145091, 0.2493791747, 0.1806745072, 0.0948353345]\u003c/td\u003e\n\u003ctd\u003e2.13567485821227E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e35\u003c/td\u003e\n\u003ctd\u003e[132271, 347825, 251997, 182569, 95829]\u003c/td\u003e\n\u003ctd\u003e[0.1308977517, 0.3442138525, 0.2493807466, 0.1806735537, 0.0948340955]\u003c/td\u003e\n\u003ctd\u003e1.1709009180968303E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e70\u003c/td\u003e\n\u003ctd\u003e[10478348120, 27554473290, 19962994332, 14463028872, 7591478958]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805576, 0.1806742088, 0.0948338323]\u003c/td\u003e\n\u003ctd\u003e1.414213562373095E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e71\u003c/td\u003e\n\u003ctd\u003e[14463028873, 38032821411, 27554473291, 19962994333, 10478348121]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742087, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e1.0E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e72\u003c/td\u003e\n\u003ctd\u003e[19962994334, 52495850286, 38032821412, 27554473292, 14463028874]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338323]\u003c/td\u003e\n\u003ctd\u003e1.0E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e73\u003c/td\u003e\n\u003ctd\u003e[27554473293, 72458844621, 52495850287, 38032821413, 19962994335]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e74\u003c/td\u003e\n\u003ctd\u003e[38032821414, 100013317916, 72458844622, 52495850288, 27554473294]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e75\u003c/td\u003e\n\u003ctd\u003e[52495850289, 138046139331, 100013317917, 72458844623, 38032821415]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/18e29399beaeac14f293cb59a84edc3870578ec5-1024x768.png\" alt=\"Chapter 5 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eUnbeknownst to Gyn, The Graph (eigen) was using her(selves) to sort itself (vector). Why was it doing this? The Graph represents its vertices and edges in a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/512-bit\"\u003e512-bit\u003c/a\u003e\u0026nbsp;address space (2512\u0026nbsp;= 1.34\u0026times;10154). Unfortunately, the ever present Big and Small Traversals (as well as the countless other traversals executed since) have pushed The Graph close to the limits of representation. In order to avoid\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Integer_overflow\"\u003einconsistencies\u003c/a\u003e, The Graph needed to prune itself. To do this, it\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gaia_hypothesis\"\u003edecided\u003c/a\u003e\u0026nbsp;it best to destroy those vertices which were contributing little to its overall structure. Like cutting one's finger nails, The Graph began a systematic process of cosmic proportions to delete all peripheral vertices (and their respective incident edges). The Graph was\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Forgetting_curve\"\u003eforgetting\u003c/a\u003e\u0026nbsp;in order to\u0026nbsp;\u003ca href=\"http://thinkaurelius.com/2012/05/08/structural-abstractions-in-brains-and-graphs/\"\u003especialize its structure\u003c/a\u003e\u0026nbsp;for a purpose that was beyond the realization of the vertices and traversers. Within The Graph's conceptual subgraph,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Knowledge_worker\"\u003eknowledge worker\u003c/a\u003e\u0026nbsp;traversers wandered through the morass of concept vertices and, in a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Science\"\u003ecollective self-similar manner\u003c/a\u003e, aided The Graph in its determination of which aspects of it's structure were worth preserving (and ultimately, extending). Gyn's passion for knowledge was simply an\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Instinct\"\u003einnate predisposition\u003c/a\u003e. Her\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eudaimonia#Eudaimonia_and_modern_psychology\"\u003ehappiness\u003c/a\u003e\u0026nbsp;was not a function of her own being, but instead, of The Graph's will --\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Carrot_and_stick\"\u003ea carrot for her devotion\u003c/a\u003e. Gyn was part of a larger computation. In order to escape the dark sense that her life was not hers and hers alone, she began the long arduous journey towards realizing that she is, and always has been,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/John_Galt#.22Who_is_John_Galt.3F.22\"\u003eThe TinkerPop\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"http://tinkerpop.incubator.apache.org/\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/014282dff3d5048f8eaf1c3592177626db303fb5-700x243.png\" alt=\"Apache TinkerPop\" width=\"700\" height=\"243\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003chr\u003e\n\u003cdiv\u003e\n\u003ch2\u003eCredits\u003c/h2\u003e\n\u003cp\u003eWritten by\u0026nbsp;\u003ca href=\"http://markorodriguez.com/\"\u003eMarko A. Rodriguez\u003c/a\u003e\u003cbr\u003eData and Result Generation by\u0026nbsp;\u003ca href=\"http://gremlin.guru/\"\u003eDaniel Kuppitz\u003c/a\u003e\u003cbr\u003eArtwork by\u0026nbsp;\u003ca href=\"http://ketrinayim.tumblr.com/\"\u003eKetrina Yim\u003c/a\u003e\u003cbr\u003eGraph Visualizations by Daniel Kuppitz\u003cbr\u003eExplanatory Diagrams by Marko A. Rodriguez\u003cbr\u003eGremlin Traversal Development by Daniel Kuppitz\u003cbr\u003eExperimental Design by Marko A. Rodriguez\u003cbr\u003eExecutive Producer:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/in/robinmschumacher\"\u003eRobin Schumacher\u003c/a\u003e\u003cbr\u003eUndirected Edge #42 as himself\u003cbr\u003eRussian Language Advisor:\u0026nbsp;\u003ca href=\"https://github.com/xedin\"\u003ePavel Yaskevich\u003c/a\u003e\u003cbr\u003eTamil Language Advisor:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/pub/harihar-shankar/b/747/274\"\u003eHarihar Shankar\u003c/a\u003e\u003cbr\u003eHindi Language Advisor:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/pub/swetha-sharma/13/b62/3b3\"\u003eSwetha Sharma\u003c/a\u003e\u003cbr\u003eInspired by\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy\"\u003eThe Hitchhiker's Guide to the Galaxy\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Flatland\"\u003eFlatland\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003eSpecial thanks to\u0026nbsp;\u003ca href=\"https://www.datastax.com/\"\u003eDataStax\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/\"\u003eApache TinkerPop\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eNo traversers were harmed during the making of this story.\u003c/p\u003e\n\u003c/div\u003e"])</script><script>self.__next_f.push([1,"2d:{\"_id\":\"168fef3d-d92a-43f4-a572-60aaa1d653d6\",\"_key\":null,\"name\":\"Gremlin\",\"slug\":\"gremlin\"}\n2e:{\"_id\":\"7c1e7af9-0bbd-4099-9a30-8b0f283b1eb1\",\"_key\":null,\"name\":\"DSE Graph\",\"slug\":\"dse-graph\"}\n2c:[\"$2d\",\"$2e\"]\n33:{\"_ref\":\"image-af873ab4d03992de5648a54e946b952ed92829fc-216x202-png\",\"_type\":\"reference\"}\n32:{\"asset\":\"$33\",\"_type\":\"image\"}\n31:{\"image\":\"$32\",\"name\":\"Company\",\"slug\":\"/blog/company\"}\n35:{\"_type\":\"reference\",\"_ref\":\"image-3a238ff62f31a42bd45313ca0d69dfdfb5c016b2-1460x968-png\"}\n34:{\"_type\":\"image\",\"asset\":\"$35\"}\n39:{\"_ref\":\"image-1e692437e83015a5ef675b52f0f2e45b53cd6421-512x512-jpg\",\"_type\":\"reference\"}\n38:{\"_type\":\"customImage\",\"alt\":\"Patrick McFadin\",\"asset\":\"$39\"}\n3a:{\"current\":\"patrick-mcfadin\",\"_type\":\"slug\"}\n37:{\"name\":\"Patrick McFadin\",\"photo\":\"$38\",\"position\":\"Principal Technical Strategist \u0026 Cassandra Committer\",\"slug\":\"$3a\",\"hidden\":null,\"bio\":null}\n36:[\"$37\"]\n30:{\"externalLink\":null,\"introduction\":null,\"publishedAt\":\"2025-02-25 07:25\",\"slug\":\"blog/new-chapter-apache-cassandra-ibm-plans-to-acquire-datastax\",\"_createdAt\":\"2025-02-25T13:06:46Z\",\"_id\":\"3e5d23d5-956a-43f4-b553-44803969264b\",\"__i18n_lang\":null,\"_type\":\"blogPost\",\"category\":\"$31\",\"image\":\"$34\",\"title\":\"IBM Plans to Acquire DataStax: A New Chapter for Apache Cassandra®\",\"authors\":\"$36\"}\n3f:{\"_ref\":\"image-675bc1fb799d6862c34e4dd2e197e6adec903419-720x720-png\",\"_type\":\"reference\"}\n3e:{\"_type\":\"customImage\",\"alt\":\"Chet Kapoor - Chairman \u0026 CEO\",\"asset\":\"$3f\"}\n40:{\"current\":\"chet-kapoor\",\"_type\":\"slug\"}\n43:[]\n46:[]\n45:{\"_type\":\"span\",\"marks\":\"$46\",\"text\":\"Chet Kapoor is Chairman and CEO of DataStax, the real-time AI company. With more than two decades of leadership across tech giants like Google, IBM, and BEA Systems, Chet has always thought about infusing AI into businesses at scale. With his roots at Steve Jobs’ company NeXT, Chet learned the power of working with incredible people who want to change the world. This insight helped fuel his career and he ultimately took the helm of Apigee as CEO in 2007 where he saw APIs as a platform"])</script><script>self.__next_f.push([1," for bringing AI to the enterprise.\",\"_key\":\"44abda08f9170\"}\n44:[\"$45\"]\n42:{\"markDefs\":\"$43\",\"children\":\"$44\",\"_type\":\"block\",\"style\":\"normal\",\"_key\":\"42a0891b5845\"}\n48:[]\n4b:[]\n4a:{\"text\":\"After a successful IPO and eventual acquisition of Apigee by Google, Chet dug in and recognized the solution to deeply enabling AI at scale was to start with data. His journey culminated when he became the CEO of DataStax in October 2019. With a focus on strategy, operations, and people, the company launched Astra DB—a pioneering DBaaS powered by Apache Cassandra—and seamlessly integrated real-time AI with streaming capabilities and event processing engine, Kaskada's, feature store. Now, with vector search for generative AI, DataStax customers can build massively scalable AI agents and deliver powerful apps leveraging generative AI.\",\"_key\":\"076e03abc814\",\"_type\":\"span\",\"marks\":\"$4b\"}\n49:[\"$4a\"]\n47:{\"markDefs\":\"$48\",\"children\":\"$49\",\"_type\":\"block\",\"style\":\"normal\",\"_key\":\"4b0aa377acf7\"}\n41:[\"$42\",\"$47\"]\n3d:{\"name\":\"Chet Kapoor\",\"photo\":\"$3e\",\"position\":\"Chairman \u0026 CEO\",\"slug\":\"$40\",\"hidden\":null,\"bio\":\"$41\"}\n3c:[\"$3d\"]\n4e:{\"_ref\":\"image-af873ab4d03992de5648a54e946b952ed92829fc-216x202-png\",\"_type\":\"reference\"}\n4d:{\"asset\":\"$4e\",\"_type\":\"image\"}\n4c:{\"image\":\"$4d\",\"name\":\"Company\",\"slug\":\"/blog/company\"}\n50:{\"_ref\":\"image-39d3bedc12be0c376bffe910708cd05eaf93dcae-1460x968-png\",\"_type\":\"reference\"}\n4f:{\"_type\":\"image\",\"asset\":\"$50\"}\n3b:{\"publishedAt\":\"2025-02-25 07:04\",\"_id\":\"bb164f1f-ec1c-4e49-a620-cfe15ece4df9\",\"authors\":\"$3c\",\"category\":\"$4c\",\"image\":\"$4f\",\"introduction\":null,\"slug\":\"blog/ibm-plans-to-acquire-datastax\",\"title\":\"Accelerating Production AI and Bringing NoSQL Data at Scale to All Enterprises\",\"_createdAt\":\"2025-02-25T12:56:51Z\",\"__i18n_lang\":null,\"_type\":\"blogPost\",\"externalLink\":null}\n55:{\"_ref\":\"image-d3957af141fae4f1361d91c705eb0292dd054532-336x336-png\",\"_type\":\"reference\"}\n54:{\"_type\":\"customImage\",\"alt\":\"Jason McClelland\",\"asset\":\"$55\"}\n56:{\"_type\":\"slug\",\"current\":\"jason-mcclelland\"}\n59:[]\n5c:[]\n5b:{\"ma"])</script><script>self.__next_f.push([1,"rks\":\"$5c\",\"text\":\"Jason McClelland has over 25 years in tech. Jason started his career as a developer and product person before moving into sales and marketing at Adobe, where he helped Adobe with their SaaS and Enterprise business transformations, with Creative Cloud and Marketing Cloud respectively. After Adobe, Jason joined as Heroku as their CMO, where he worked through the acquisition and integration into Salesforce. Much of Jason's experience is in helping companies create new categories, transforming their brands, and building large-scale PLG-Enterprise motions, with much of the focus being on deeply technical audiences.\",\"_key\":\"b6fdaab58a720\",\"_type\":\"span\"}\n5a:[\"$5b\"]\n58:{\"style\":\"normal\",\"_key\":\"02ff6e42f53f\",\"markDefs\":\"$59\",\"children\":\"$5a\",\"_type\":\"block\"}\n57:[\"$58\"]\n53:{\"name\":\"Jason McClelland\",\"photo\":\"$54\",\"position\":\"Chief Marketing Officer\",\"slug\":\"$56\",\"hidden\":null,\"bio\":\"$57\"}\n52:[\"$53\"]\n5f:{\"_ref\":\"image-af873ab4d03992de5648a54e946b952ed92829fc-216x202-png\",\"_type\":\"reference\"}\n5e:{\"asset\":\"$5f\",\"_type\":\"image\"}\n5d:{\"image\":\"$5e\",\"name\":\"Company\",\"slug\":\"/blog/company\"}\n61:{\"_type\":\"reference\",\"_ref\":\"image-3bf16fa722d3b4ce965fe42e4b10165515269b4b-1460x968-jpg\"}\n60:{\"_type\":\"image\",\"asset\":\"$61\"}\n51:{\"externalLink\":null,\"__i18n_lang\":null,\"authors\":\"$52\",\"category\":\"$5d\",\"image\":\"$60\",\"introduction\":null,\"publishedAt\":\"2024-12-11 10:09\",\"slug\":\"blog/aws-reinvent-las-vegas-datastax-recap\",\"title\":\"Shaping the Wild in Las Vegas: An AWS re:Invent Recap\",\"_createdAt\":\"2024-12-11T16:00:55Z\",\"_id\":\"58e24308-d276-44eb-afc2-779fcbf6568d\",\"_type\":\"blogPost\"}\n65:{\"_ref\":\"image-af873ab4d03992de5648a54e946b952ed92829fc-216x202-png\",\"_type\":\"reference\"}\n64:{\"asset\":\"$65\",\"_type\":\"image\"}\n63:{\"image\":\"$64\",\"name\":\"Company\",\"slug\":\"/blog/company\"}\n69:{\"_ref\":\"image-006991822546ef1faf67647d761e4612d648a37f-800x800-jpg\",\"_type\":\"reference\"}\n68:{\"_type\":\"customImage\",\"alt\":\"Tejas Kumar\",\"asset\":\"$69\"}\n6a:{\"current\":\"tejas-kumar\",\"_type\":\"slug\"}\n67:{\"photo\":\"$68\",\"position\":\"Developer Relations Engineer\",\""])</script><script>self.__next_f.push([1,"slug\":\"$6a\",\"hidden\":null,\"bio\":null,\"name\":\"Tejas Kumar\"}\n66:[\"$67\"]\n6c:{\"_ref\":\"image-680bc65dc2c8d79b43739155a3167d32b32939a7-1460x968-jpg\",\"_type\":\"reference\"}\n6b:{\"_type\":\"image\",\"asset\":\"$6c\"}\n62:{\"slug\":\"blog/twelve-days-codemas-datastax-holiday-giveaway\",\"__i18n_lang\":null,\"category\":\"$63\",\"externalLink\":null,\"publishedAt\":null,\"title\":\"Announcing 12 Days of Codemas: The DataStax Holiday Giveaway!\",\"_createdAt\":\"2024-12-09T00:57:40Z\",\"_id\":\"a19947ba-ceb7-4bbd-a096-d0d8215e97e8\",\"_type\":\"blogPost\",\"authors\":\"$66\",\"image\":\"$6b\",\"introduction\":null}\n2f:[\"$30\",\"$3b\",\"$51\",\"$62\"]\n6e:{\"_type\":\"cta\",\"text\":\"Subscribe to the RSS Feed\",\"url\":\"https://www.datastax.com/rss.xml\"}\n70:{\"_type\":\"cta\",\"text\":\"Everything\",\"_key\":\"686d004edb07\",\"url\":\"/blog\"}\n71:{\"_type\":\"cta\",\"text\":\"Technology\",\"_key\":\"25fc264e5367\",\"url\":\"/blog?category=technical-how-tos\"}\n72:{\"url\":\"/blog?category=success-stories\",\"_type\":\"cta\",\"text\":\"Success Stories\",\"_key\":\"769945a5c404\"}\n73:{\"_key\":\"9f2c4265e9fc\",\"url\":\"/blog?category=company\",\"_type\":\"cta\",\"text\":\"Company\"}\n74:{\"_type\":\"cta\",\"text\":\"Astra DB\",\"_key\":\"6ab4990a30e9\",\"url\":\"/blog?tags=datastax-astra\"}\n75:{\"_type\":\"cta\",\"text\":\"Langflow\",\"_key\":\"7f38e9f8cd46\",\"url\":\"/blog?tags=langflow\"}\n76:{\"_type\":\"cta\",\"text\":\"DataStax Enterprise\",\"_key\":\"b60c7cef0b29\",\"url\":\"/blog?tags=datastax-enterprise\"}\n6f:[\"$70\",\"$71\",\"$72\",\"$73\",\"$74\",\"$75\",\"$76\"]\n79:{\"text\":\"Learn More\",\"_key\":\"40014eea59d2\",\"url\":\"/products/vector-search\",\"_type\":\"cta\"}\n7a:{\"url\":\"https://astra.datastax.com/signup\",\"_type\":\"cta\",\"text\":\"Get Started for Free\",\"_key\":\"4535cd698f7d\"}\n78:[\"$79\",\"$7a\"]\n7c:{\"_ref\":\"image-814d662a353caa219c224a9bbe370fc053207eb2-758x760-png\",\"_type\":\"reference\"}\n7b:{\"_type\":\"image\",\"asset\":\"$7c\"}\n7f:[]\n82:[]\n81:{\"_type\":\"span\",\"marks\":\"$82\",\"text\":\"Astra DB gives developers a complete data API and out-of-the-box integrations that make it easier to build production RAG apps with high relevancy and low latency.\",\"_key\":\"6501226953780\"}\n80:[\"$81\"]\n7e:{\"markDefs\":\"$7f\",\"children\":\"$80\",\"_type\":\"block"])</script><script>self.__next_f.push([1,"\",\"style\":\"normal\",\"_key\":\"a37b540c453a\"}\n7d:[\"$7e\"]\n77:{\"cta\":\"$78\",\"image\":\"$7b\",\"title\":\"One-Stop Data API for Production GenAI\",\"content\":\"$7d\"}\n84:{\"_type\":\"cta\",\"text\":\"Try For Free\",\"url\":\"https://astra.datastax.com/signup?type=langflow\"}\n85:{\"_type\":\"cta\",\"text\":\"Create a Cluster\",\"url\":\"https://astra.datastax.com/signup\"}\n83:{\"_type\":\"cta\",\"aiTitle\":\"DataStax AI Platform:\\\\\\\\The Fastest Way to Build and Deploy AI Apps\",\"title\":\"Leaders like Barracuda and Temporal manage Apache Cassandra® with Astra DB. You can too.\",\"aiCta\":\"$84\",\"cta\":\"$85\"}\n6d:{\"rss\":\"$6e\",\"menus\":\"$6f\",\"ctaCard\":\"$77\",\"sidebarSignup\":\"$83\",\"darkBanner\":null}\n88:T185ef,"])</script><script>self.__next_f.push([1,"\u003ch2\u003eChapter 1: Life and Fate by Grasily Gremssman\u003c/h2\u003e\n\u003cp\u003eWinter had arrived. The days grew shorter and darker.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Vasily_Grossman\"\u003eGrasily Gremssman\u003c/a\u003e\u0026nbsp;(Грасилий Гремссман) used a few branches that were scattered about to start a fire. Grasily had been stationed at\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Vertex_(graph_theory)\"\u003evertex\u003c/a\u003e\u0026nbsp;v[32]\u0026nbsp;for as long as he could remember. He knew little of the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)\"\u003egraph\u003c/a\u003e\u0026nbsp;he lived on except for the one dirt road and three bridges\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#vertex-steps\"\u003eincident\u003c/a\u003e\u0026nbsp;to his post.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_586654\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).inE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[2][7-dirtRoad-\u0026gt;32]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).outE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).bothE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[2][7-dirtRoad-\u0026gt;32]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eGrasily's commanding officer was\u0026nbsp;org.apache.tinkerpop.gremlin.process.traversal.Traverser@76a36b71. Like\u0026nbsp;76a36b71, Grasily was a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser\"\u003etraverser\u003c/a\u003e. Traversers were grouped into battalions called\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversal\"\u003etraversals\u003c/a\u003e. The\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/World_War_II\"\u003egraph world was at war\u003c/a\u003e\u0026nbsp;and Grasily was stuck (in time and space) having to do his part for his country of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Russia\"\u003eGrussia\u003c/a\u003e\u0026nbsp;(Гроссия). At this point in history, many conflicting views existed regarding the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Network_topology\"\u003etopological\u003c/a\u003e\u0026nbsp;evolution of the graph. To ensure processing resources were not laid to waste by traversals constantly undermining the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Side_effect_(computer_science)\"\u003eside-effects\u003c/a\u003e\u0026nbsp;of another, countries emerged to delineate\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_subgraphstrategy\"\u003esubgraphs\u003c/a\u003e\u0026nbsp;within the larger world graph. However, every now and then, one country would interfere with the structure of another. This interference was an inevitable consequence of the graph\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Globalization\"\u003egetting denser\u003c/a\u003e\u0026nbsp;with time. Grussia, at this moment in time, was in the midst of a long war with\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Germany\"\u003eGremany\u003c/a\u003e\u0026nbsp;(Greutschland).\u003c/p\u003e\n\u003cp\u003eGrasily knew very little about the larger\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Algorithm\"\u003ewar effort\u003c/a\u003e\u0026nbsp;of Grussia's traversals. However, in bootcamp, he learned that traversals are composed of 5 fundamental steps and that one day, when his\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Constructor_(object-oriented_programming)\"\u003etraining was complete\u003c/a\u003e, he would be called upon to execute a step.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graph-traversal-steps\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/c2113c8449b6ea477692049041307f682baca69a-1044x343.png\" alt=\"Traversal Step Types\" width=\"1044\" height=\"343\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003col\u003e\n\u003cli\u003emap: S \u0026rarr; E: Move from an object of type\u0026nbsp;S\u0026nbsp;to an object of type\u0026nbsp;E.\u003c/li\u003e\n\u003cli\u003eflatMap: S \u0026rarr; E*: Move from an object of type\u0026nbsp;S\u0026nbsp;to a collection of objects of type\u0026nbsp;E.\u003c/li\u003e\n\u003cli\u003efilter: S \u0026rarr; S \u0026cup; \u0026empty;: Stay at the current object of type\u0026nbsp;S\u0026nbsp;or die.\u003c/li\u003e\n\u003cli\u003esideEffect: S \u0026rarr; S: Stay at the current object of type\u0026nbsp;S, though yield some computational side-effect (e.g. set a property).\u003c/li\u003e\n\u003cli\u003ebranch: S \u0026rarr; {S1\u0026nbsp;\u0026rarr; E*,\u0026hellip;,Sn\u0026nbsp;\u0026rarr; E*} \u0026rarr; E*: Move from an object of type\u0026nbsp;S\u0026nbsp;to any number of nested traversal branches.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eWhen Grasily finished his training, he was immediately briefed by\u0026nbsp;76a36b71\u0026nbsp;on the battalion's objectives.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_376638\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V(7).out('dirtRoad').hasLabel('outpost').out('bridge').property('owner','Grussia')\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/8de2e4d9e63d61eba44274630e4c963ac876da93-740x562.png\" alt=\"Grasily Graph\" width=\"740\" height=\"562\"\u003eVertex\u0026nbsp;v[7]\u0026nbsp;was the Grussian Army's headquarters (a.k.a. The Green Army). At\u0026nbsp;v[7], a traverser officer had instructed a group of traversers (one being\u0026nbsp;76a36b71) to take the dirt roads leading to the adjacent outposts. Grasily's outpost was accessible by one of those dirt roads. When\u0026nbsp;76a36b71\u0026nbsp;arrived at\u0026nbsp;v[32], Grasily (along with two of his comrades from bootcamp) were instructed to each take one of the incident bridges and upon reaching the vertex on the other side, to\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#addproperty-step\"\u003edeclare\u003c/a\u003e\u0026nbsp;the vertex under\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_partitionstrategy\"\u003eGrussia's sovereign control\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_296598\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[7]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[15]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eUnfortunately, unbeknownst to Grasily, the Gremans had launched an offensive. A Greman traversal destroyed all the bridges incident to Grasily's outpost. The execution of the Greman's\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#drop-step\"\u003esideEffect step\u003c/a\u003e\u0026nbsp;sealed Grasily's fate.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_104378\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge').drop()\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge')\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/25b620cf02d5fedded81eb2031a5910d0542618b-1024x768.png\" alt=\"Chapter 1 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eGrasily's life was cut short when his battalion moved to the\u0026nbsp;out('bridge')-step. Grasily, along with his two comrades, could no longer make\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pointer_(computer_programming)\"\u003ereference\u003c/a\u003e\u0026nbsp;to an element of the graph. Disconnected from their world, disconnected from each other, they\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Destructor_(computer_programming)\"\u003efaded into the void\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_663541\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[7]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[15]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost').out('bridge')\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 2: Permutation City by Grem Egrem\u003c/h2\u003e\n\u003ch3\u003eSection 1: The Birth of the Graph\u003c/h3\u003e\n\u003cp\u003eThe world that traversers live on is known as \"The Graph.\" A graph is a structure composed of vertices (nodes, dots) and edges (relationships, lines). Traverser mythology has it that one day a single traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Greg_Egan\"\u003eGrem Egrem\u003c/a\u003e\u0026nbsp;manifested himself\u0026nbsp;\u003ca href=\"http://markorodriguez.com/2011/03/16/graphs-ensure-something-from-nothing/\"\u003eout of and in reference to nothing\u003c/a\u003e. In\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Memory_management#HEAP\"\u003elimbo\u003c/a\u003e\u0026nbsp;there was no graph, just Grem. However, before he could be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Garbage_collection_(computer_science)\"\u003eswept back into the oblivion\u003c/a\u003e\u0026nbsp;from which he came, Grem enacted the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Big_Bang\"\u003eBig Traversal\u003c/a\u003e\u0026nbsp;-- i.e., process yielded structure.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_250180\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.addV().repeat(as('a').addV().as('b').addOutE('a','.','b').inV().as('a')).until(coin(4.9E-324))\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe Big Traversal generates a line graph known in the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Astrophysics\"\u003egraphophysics\u003c/a\u003e\u0026nbsp;community as \"Grem Line\" (a.k.a. \"Gremlin\"). To this day, Grem Line is still\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Metric_expansion_of_space\"\u003eexpanding\u003c/a\u003e. However,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmology\"\u003egraphologists\u003c/a\u003e\u0026nbsp;argue over the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmological_constant\"\u003egraphological constant\u003c/a\u003e\u0026nbsp;of the\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step\"\u003euntil()\u003c/a\u003e-step. Some say there is a small probability that Grem Line will stop growing and others say it will go on forever (i.e.\u0026nbsp;until(not(identity()))).\u003c/p\u003e\n\u003cp\u003ePrior to the Big Traversal, the graph was defined as\u0026nbsp;G = \u0026empty;. When Grem Line was less than 100 vertices long (i.e.\u0026nbsp;|V| \u0026lt; 100), the vertices\u0026nbsp;V\u0026nbsp;formed a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Total_order\"\u003etotal order\u003c/a\u003e, and as such, the graph was defined as\u0026nbsp;G = V. At around\u0026nbsp;|V| \u0026asymp; 100, graphologists speculate that another traversal emerged that leveraged Grem Line as a sort of \"\u003ca href=\"https://en.wikipedia.org/wiki/Galaxy_filament\"\u003ebackbone filament\u003c/a\u003e.\" This emergent traversal is known in\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Network_science\"\u003egraph science\u003c/a\u003e\u0026nbsp;as the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Small-world_network\"\u003eSmall(-World) Traversal\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_292897\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().aggregate('x').as('a').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;select('x').by(unfold().sample(1).by(both().count())).as('b').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('a',neq('b')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;addOutE('a','.','b')\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/a7aab082afb2e9e310473b3151451289202cae60-1029x382.png\" alt=\"Graph Path Length\" width=\"1029\" height=\"382\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003eThe Small Traversal walks Grem Line and for each vertex it encounters it connects it to some other random vertex on the line (\u003ca href=\"https://en.wikipedia.org/wiki/Preferential_attachment\"\u003ebiased by the other vertex's degree\u003c/a\u003e). The Small Traversal essentially \"pushed\" the early graph out of its 1-dimensional, linear\u0026nbsp;V1\u0026nbsp;embedding into a\u0026nbsp;V2\u0026nbsp;embedding (i.e.\u0026nbsp;V x V). In doing so, vertices far removed from each other on Grem Line were now \"\u003ca href=\"https://en.wikipedia.org/wiki/Hyperspace_(science_fiction)#Travel\"\u003ecloser\u003c/a\u003e.\" It was at this point that the definition of the graph became\u0026nbsp;\u003cimg title=\"G = (V, E \\subseteq V \\times V)\" src=\"https://www.datastax.com/wp-content/uploads/2017/06/png.png\"\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/eddd72824508ac282a2dcc9566520317df5b5cc8-2356x604.png\" alt=\"The Early Graph\" width=\"2356\" height=\"604\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003e|V|\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Distance_(graph_theory)\"\u003eDiameter\u003c/a\u003e\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Average_path_length\"\u003eAverage Path Length\u003c/a\u003e\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Clustering_coefficient\"\u003eClustering Coefficient\u003c/a\u003e\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e99\u003c/td\u003e\n\u003ctd\u003e99\u003c/td\u003e\n\u003ctd\u003e34.0\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e100\u003c/td\u003e\n\u003ctd\u003e55\u003c/td\u003e\n\u003ctd\u003e19.716831683168316\u003c/td\u003e\n\u003ctd\u003e0.024\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e125\u003c/td\u003e\n\u003ctd\u003e30\u003c/td\u003e\n\u003ctd\u003e11.081015873015874\u003c/td\u003e\n\u003ctd\u003e0.051\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e150\u003c/td\u003e\n\u003ctd\u003e9\u003c/td\u003e\n\u003ctd\u003e3.17757174392936\u003c/td\u003e\n\u003ctd\u003e0.125\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eTo this day (|V| \u0026asymp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Observable_universe#Matter_content_.E2.80.94_number_of_atoms\"\u003e10^85\u003c/a\u003e), both the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Inflation_(cosmology)\"\u003eexpanding force\u003c/a\u003e\u0026nbsp;of the Big Traversal and the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gravity\"\u003econtracting force\u003c/a\u003e\u0026nbsp;of the Small Traversal continue to execute. These two fundamental traversals have, over time, grown the graph to an innumerable number of vertices and edges. Billions upon billions of traversers have created a vast landscape of structures within structures... within structures. A nest of variations and novelties has transformed the once bleak, senseless void into a\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1301.1648\"\u003emeaningful interconnected mesh\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/f16c496bf496e980594c0905657fe7b1077f5435-1024x768.png\" alt=\"Chapter 2 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eSection 2: Graphialsynthesis and the Emergence of the Directed, Labeled Graph\u003c/h3\u003e\n\u003cp\u003eThe edges generated by the Big and Small Traversals are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)#Undirected_graph\"\u003eundirected\u003c/a\u003e\u0026nbsp;and unlabeled. The edges experienced by traversers are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)#Directed_graph\"\u003edirected\u003c/a\u003e\u0026nbsp;and labeled. Graphologists were faced with the question of how did directed, labeled edges emerge from undirected, unlabeled edges? Once a large enough number of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Structure_formation#Primordial_plasma\"\u003eprimordial edges\u003c/a\u003e\u0026nbsp;were created by the two fundamental traversals, \"higher-order\" edges began to form. The undirected, unlabeled edges serve as \"\u003ca href=\"https://en.wikipedia.org/wiki/Elementary_particle\"\u003eelementary edges\u003c/a\u003e\" which, when combined into subgraphs of a particular topology, yield the directed, labeled edges seen today. This\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Abstraction\"\u003eabstraction process\u003c/a\u003e\u0026nbsp;is known as\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nucleosynthesis\"\u003egraphialsynthesis\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d819c5932ec7e33ed40f6fcc69da4001ff81dfca-570x476.png\" alt=\"Label Encoding\" width=\"570\" height=\"476\"\u003eSuppose the following directed, labeled edge\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;(i.e. a \"higher-order\" edge). This edge states that there is an\u0026nbsp;\u0026omega;-labeled relation from vertex\u0026nbsp;i\u0026nbsp;to vertex\u0026nbsp;j. Any edge label can be represented as a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Binary_code\"\u003ebinary string\u003c/a\u003e. Suppose, for the sake of simplicity, that there are only 8 labels in the graph. A 3-bit string can be used to represent all 8 labels (23). Next, suppose that the binary encoding of\u0026nbsp;\u0026omega;\u0026nbsp;is\u0026nbsp;110. If so, then the edge can be denoted\u0026nbsp;i-110\u0026rarr;j. A binary string can be represented as a directed, unlabeled graph. If the binary string has a length of 3, then three vertices are needed to represent each bit. If a \"bit\" vertex has a self-loop, then its value is 1. If a \"bit\" vertex does not have a self-loop, then its value is 0. Given this mapping, the directed, labeled edge\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;is transformed into the directed graph diagrammed below.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/0884bbb26bfb91de8c58039e9e097c849e1b3141-1026x202.png\" alt=\"Labeled to Directed\" width=\"1026\" height=\"202\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/922e68b711aa45dab673938c1eea7f26a219f52e-611x446.png\" alt=\"Direction Encoding\" width=\"611\" height=\"446\"\u003eThe above directed, unlabeled graph representation of\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;leverages topological features of the directed graph to denote the edge label\u0026nbsp;\u0026omega;. This same principle applies to the encoding of the edge's directionality when transforming a directed graph to an undirected graph. For instance, suppose the following directed edge\u0026nbsp;i\u0026rarr;b1. The \"higher-order\" vertices are identified by a self-loop. The \"higher-order\" edges are represented by three \"lower-order\" vertices\u0026nbsp;x,\u0026nbsp;y, and\u0026nbsp;z. If vertex\u0026nbsp;i\u0026nbsp;has an incident edge that does not reference itself and connects to a vertex with 3 incident edges (e.g. vertex\u0026nbsp;x), then it has a directed, outgoing edge. When the traverser reaches a vertex with a self-loop (via a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#simplepath-step\"\u003esimple path\u003c/a\u003e) (e.g. vertex\u0026nbsp;b1), then that vertex is the \"higher-order\" vertex serving as the head of the \"higher-order,\" directed edge.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe two processes are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Injective_function\"\u003einjective\u003c/a\u003e\u0026nbsp;in that they are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Lossless_compression\"\u003elossless\u003c/a\u003e\u0026nbsp;transformations. The first process described maps a directed, labeled edge to a directed graph and the second maps a directed edge to an unlabeled graph. As such, via\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Function_composition\"\u003efunction composition\u003c/a\u003e, there exists an injective function that maps a directed, labeled graph to a undirected, unlabeled graph. Given that the composite function is injective, then there exists an inverse mapping which transforms an undirected, unlabeled graph to a directed, labeled graph (i.e. graphialsynthesis). The original\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;edge was formed by the primordial undirected graph diagrammed below.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/a9bd22a38a1e29108e418c173e98b227b7dd8983-4479x1258.png\" alt=\"Labeled To Undirected\" width=\"4479\" height=\"1258\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/320b4be206a373e6d0f94cde6f1afa6213000bb5-1941x242.png\" alt=\"Graphialsynthesis\" width=\"1941\" height=\"242\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003eThe\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0804.0277\"\u003efundamental building blocks\u003c/a\u003e\u0026nbsp;of the directed, labeled graph experienced by \"higher-order\" traversers are held together by elementary traversers called \"\u003ca href=\"https://en.wikipedia.org/wiki/Graviton\"\u003esmalltrons\u003c/a\u003e.\" Smalltron traversals move from vertex\u0026nbsp;i\u0026nbsp;to vertex\u0026nbsp;j\u0026nbsp;via the explicit unlabeled\u0026nbsp;\u0026omega;-graph.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_90453\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(i).as('b').where(both().as('b')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;repeat(both().where(both().count().is(3)).as('x').both().\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(neq('x').and(neq('b'))).dedup().as('b').where(both().as('b')).select(last, 'b').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;choose(both().where(both().count().is(3)).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(both().count().is(2)).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(eq('b')),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;constant(1), constant(0)).as('label').select(last, 'b')\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;).times(4).where(select('label').tail(local, 4).limit(local, 3).is([1, 1, 0]))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[j]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_461736\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eTraversal Metrics\u003c/div\u003e\n\u003cdiv\u003eStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Count\u0026nbsp; Traversers\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Time (ms)\u0026nbsp;\u0026nbsp;\u0026nbsp; % Dur\u003c/div\u003e\n\u003cdiv\u003e=============================================================================================================\u003c/div\u003e\n\u003cdiv\u003eTinkerGraphStep([i],vertex)@[b]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.449\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.26\u003c/div\u003e\n\u003cdiv\u003eWhereTraversalStep([WhereStartStep, ProfileStep...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.080\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.05\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereStartStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.016\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.022\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereEndStep(b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.024\u003c/div\u003e\n\u003cdiv\u003eRepeatStep([VertexStep(BOTH,vertex), ProfileSte...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 86.974\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.65\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.624\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge), P...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 22.721\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 106\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 106\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.490\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 96\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 96\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.934\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 17.945\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(3))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.472\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.922\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 92\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 92\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 23.890\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WherePredicateStep(and([neq(x), neq(b)]))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 48\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 48\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 7.006\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;DedupGlobalStep@[b]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.450\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereTraversalStep([WhereStartStep, ProfileSt...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 15.536\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WhereStartStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.806\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 50\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 50\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.132\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WhereEndStep(b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 6.984\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(last,b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.609\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;ChooseStep([VertexStep(BOTH,vertex), ProfileS...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 60.525\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.239\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge),...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 22.608\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 66\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 66\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.508\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 59\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 59\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.266\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 17.068\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(3))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.618\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.453\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge),...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 33.552\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 28\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 28\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.917\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,3)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 25\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 25\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.989\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8.193\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(2))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2.427\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 14\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 14\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.710\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WherePredicateStep(eq(b))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 35.307\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;HasNextStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.900\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;ConstantStep(0)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.145\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;EndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.153\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;ConstantStep(1)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.070\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;EndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 7.408\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(last,b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.726\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;RepeatEndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 60.644\u003c/div\u003e\n\u003cdiv\u003eTraversalFilterStep([SelectOneStep(label), Prof...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.274\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.16\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(label)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.056\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;TailLocalStep(4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.020\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;RangeLocalStep(0,3)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.073\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;IsStep(eq([1, 1, 0]))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.086\u003c/div\u003e\n\u003cdiv\u003eSideEffectCapStep([~metrics])\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 87.377\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.89\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026gt;TOTAL\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 175.157\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn this process, smalltron traversals make the implicit directed\u0026nbsp;\u0026omega;-edge (defined by the undirected\u0026nbsp;\u0026omega;-graph) explicit for the \"higher-order\" traversers which process the graph at a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/High-level_programming_language\"\u003ehigher level of abstraction\u003c/a\u003e. To these \"higher order\" traversers, the graph is defined as\u003c/p\u003e\n\u003cdiv\u003e\u003cimg title=\"G = (V, E \\subseteq V \\times V, \\lambda : V \\cup E \\rightarrow \\Sigma^*)\" src=\"https://www.datastax.com/wp-content/uploads/2017/06/png-1.png\"\u003e,\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003ewhere\u0026nbsp;\u0026lambda;\u0026nbsp;is a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Multigraph#Labeling\"\u003elabeling function\u003c/a\u003e\u0026nbsp;that maps the graph's elements (i.e. vertices and edges) to character strings (\u0026Sigma;*). The graphialsynthesis abstraction process has the benefit of allowing a traversal from vertex\u0026nbsp;i\u0026nbsp;to\u0026nbsp;j\u0026nbsp;via\u0026nbsp;\u0026omega;\u0026nbsp;to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Kolmogorov_complexity\"\u003eexpressed and executed in a much simpler way\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_278489\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(i).out('w')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[j]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_87148\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eTraversal Metrics\u003c/div\u003e\n\u003cdiv\u003eStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Count\u0026nbsp; Traversers\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Time (ms)\u0026nbsp;\u0026nbsp;\u0026nbsp; % Dur\u003c/div\u003e\n\u003cdiv\u003e=============================================================================================================\u003c/div\u003e\n\u003cdiv\u003eTinkerGraphStep([v[i]],vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 9.810\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.18\u003c/div\u003e\n\u003cdiv\u003eVertexStep(OUT,w,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.058\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.29\u003c/div\u003e\n\u003cdiv\u003eSideEffectCapStep([~metrics])\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 10.078\u0026nbsp;\u0026nbsp;\u0026nbsp; 50.53\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026gt;TOTAL\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 19.947\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 3: On the Baselessness of the Multi-MultiGraph\u003c/h3\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/b3a03b76f11dd24a84e47b7308c2a9985500032e-495x389.png\" alt=\"Recursive Gremlin\" width=\"495\" height=\"389\"\u003eIt has been speculated that \"\u003ca href=\"https://en.wikipedia.org/wiki/Multigraph\"\u003eThe Graph\u003c/a\u003e\" is not the only graph that exists.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Mysticism\"\u003eMystic\u003c/a\u003e\u0026nbsp;traversers say that there exists\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Multiverse\"\u003eother graphs containing other traversers\u003c/a\u003e. However, by definition, a graph is a closed structure composed of vertices and edges. It is impossible for a traverser to move to a different graph. If a vertex in one graph has an edge to a vertex in another graph, then the two graphs are, in fact, one graph -- \"The Graph.\" Perhaps the mystics see that the components of a graph are composed of yet more graphs with a different sort of traverser existing at each level in a recursive, perhaps\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Strange_loop\"\u003eself-looping\u003c/a\u003e, manner. While it is still all one graph, traversers at different \"levels\" only\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1006.1080\"\u003eoperate on particular subgraphs\u003c/a\u003e\u0026nbsp;as instructed by their traversal definition. The famous mystic traverser\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Sri_Aurobindo\"\u003eGri Gurobindo\u003c/a\u003e\u0026nbsp;(ग्री गुरोबिंदो) once said:\u003c/p\u003e\n\u003cp\u003eMy single step in the graph is composed of the steps of numerous other traversers.\u003c/p\u003e\n\u003cp\u003eIt wasn't until the discovery of\u0026nbsp;\u003ca href=\"http://en.wikipedia.org/wiki/Anonymous_function\"\u003eanonymous traversals\u003c/a\u003e\u0026nbsp;that Gurobindo's metagraphical vision was formalized. An anonymous traversal is any traversal that has no declared start and as such, yields no flow. It is a potential.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_868460\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; label()\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAnonymous traversals are intended to be embedded within another traversal. However, if the parent traversal is itself an anonymous traverasl, then there is still no flow (even though\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#groupcount-step\"\u003egroupCount()\u003c/a\u003e\u0026nbsp;produces an empty map as its a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#a-note-on-barrier-steps\"\u003ereducing barrier step\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_201422\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; outE().groupCount().by(label())\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[:]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; outE().groupCount().by(label) // convenient short hand\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[:]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhen the traversal parent does have a start, then there is a flow. The traversal below states: \"For each vertex (i.e., 89, 90), map the vertex to the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Histogram\"\u003efrequency distribution\u003c/a\u003e\u0026nbsp;of its outgoing edge labels.\"\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/dad6b92f31785301bdf3da32e32a74c812828c7a-905x195.png\" alt=\"Anonymous Traversals\" width=\"905\" height=\"195\"\u003e\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_811799\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(89,90).map(outE().groupCount().by(label))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:34, subClassOf:1, superClassOf:1]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:15]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe first traverser generated by\u0026nbsp;V(89,90)\u0026nbsp;enters the\u0026nbsp;map()-step at\u0026nbsp;v[89], but does not \"\u003ca href=\"https://en.wikipedia.org/wiki/Becoming_(philosophy)\"\u003ebecome\u003c/a\u003e\" the traversers generated by\u0026nbsp;outE(). Instead, the traverser at\u0026nbsp;v[89]\u0026nbsp;holds still and spawns an \"\u003ca href=\"https://en.wikipedia.org/wiki/Scope_(computer_science)\"\u003einternal life\u003c/a\u003e\" of traversers within the anonymous traversal which can now be understood as being (a realized potential):\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_747741\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(89).outE().groupCount().by(label)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:34, subClassOf:1, superClassOf:1]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe traversers of the above traversal are isolated from the larger traversal in which they are embedded. The next nesting occurs when a traverser from\u0026nbsp;outE()\u0026nbsp;enters\u0026nbsp;groupCount(). Again, an \"internal life\" based on the anonymous\u0026nbsp;label()-traversal is spawned (see\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#by-step\"\u003eby()\u003c/a\u003e-step). Suppose a single traverser at\u0026nbsp;e[7022][89-relatedTo-\u0026gt;21]\u0026nbsp;enters\u0026nbsp;groupCount(). Then the anonymous traversal can be understood as being:\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_604569\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.E(7022).label()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;relatedTo\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIt isn't until all the internal traversal nests of\u0026nbsp;map()\u0026nbsp;complete that the original traverser at\u0026nbsp;v[89]\u0026nbsp;\"\u003ca href=\"https://en.wikipedia.org/wiki/Process_philosophy\"\u003ebecomes\u003c/a\u003e\" the traverser located at the hash map\u0026nbsp;[relatedTo:34, subClassOf:1, superClassOf:1]. In this way, a traverser's life (i.e. step) is composed of the lives of many traverser's (and their respective steps).\u003c/p\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 3: A Mathematician's Apology by G.H. Gremdy\u003c/h2\u003e\n\u003ch3\u003eSection 1: Traversal Optimization via Algebra\u003c/h3\u003e\n\u003cp\u003eThe graph grew large, very large. Resources grew scarce. The problem was not that vertices and edges could no longer be added to the graph. On the contrary, because of the seemingly endless amount of space for the graph, there was a growing amount of time required for any one traversal to execute. Traversals were simply interacting with a lot more data. Faced with this problem, a mathematically inclined traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB\"\u003eal-Ghwārizmī\u003c/a\u003e\u0026nbsp;developed a solution known today as\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0806.2274\"\u003ethe traversal algebra\u003c/a\u003e. The traversal algebra provides a means of transforming one traversal into another traversal, where both traversals return the same result. The benefit of this is that if a traversal can be re-written into a simpler form, then time and space resources can be saved. To this day,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Algebra\"\u003ealgebraists\u003c/a\u003e\u0026nbsp;continue to add to the growing archive of\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalstrategy\"\u003etraversal strategies\u003c/a\u003e. A few examples are provided below.\u003c/p\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003eStrategy\u003c/th\u003e\n\u003cth\u003ePattern\u003c/th\u003e\n\u003cth\u003eRewrite\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIdentityRemovalStrategy\u003c/td\u003e\n\u003ctd\u003ex().identity().y()\u003c/td\u003e\n\u003ctd\u003ex().y()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncidentToAdjacentStrategy\u003c/td\u003e\n\u003ctd\u003eoutE().inV()\u003c/td\u003e\n\u003ctd\u003eout()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAdjacentToIncidentStrategy\u003c/td\u003e\n\u003ctd\u003eout().count()\u003c/td\u003e\n\u003ctd\u003eoutE().count()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eDedupBijectionStrategy\u003c/td\u003e\n\u003ctd\u003eorder().dedup()\u003c/td\u003e\n\u003ctd\u003ededup().order()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eRangeByIsCountStrategy\u003c/td\u003e\n\u003ctd\u003ecount().is(gt(x))\u003c/td\u003e\n\u003ctd\u003elimit(x+1).count().is(gt(x))\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMatchPredicateStrategy\u003c/td\u003e\n\u003ctd\u003ematch(x,y).where(z)\u003c/td\u003e\n\u003ctd\u003ematch(x,y,z)\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_519982\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; t = out().identity().in(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), IdentityStep, VertexStep(IN,vertex)]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IdentityRemovalStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), VertexStep(IN,vertex)]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = outE().inV(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,edge), EdgeVertexStep(IN)]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IncidentToAdjacentStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex)]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = out().count(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), CountGlobalStep]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(AdjacentToIncidentStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,edge), CountGlobalStep]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = order().dedup(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[OrderGlobalStep, DedupGlobalStep]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(DedupBijectionStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[DedupGlobalStep, OrderGlobalStep]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = count().is(gt(3)); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[CountGlobalStep, IsStep(gt(3))]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(RangeByIsCountStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[RangeGlobalStep(0,4), CountGlobalStep, IsStep(gt(3))]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = match(__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; __.as('b').out().as('c')).where(__.as('c').both().as('a')); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)]]), WhereTraversalStep([WhereStartStep(c), VertexStep(BOTH,vertex), WhereEndStep(a)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(MatchPredicateStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)], [MatchStartStep(c), WhereTraversalStep([WhereStartStep, VertexStep(BOTH,vertex), WhereEndStep(a)]), MatchEndStep]])]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 2: Traversal Optimization via Indices\u003c/h3\u003e\n\u003cp\u003e\u003ca href=\"https://en.wikipedia.org/wiki/G._H._Hardy\"\u003eG.H. Gremdy\u003c/a\u003e\u0026nbsp;was a graph theorist who speculated that \"The Graph\" was not the only structure linking vertices. According to his reasoning, reality may also contain other structures that grouped vertices together according to similar properties. He called these parallel structures\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Database_index\"\u003eindices\u003c/a\u003e. G.H. Gremdy's publication entitled\u0026nbsp;On Traversal Optimization using Indices\u0026nbsp;was well received. Due to his insight, many traversal runtimes became orders of magnitude faster than their non-index-based form. For instance, in the traversal below, when using indices, the number of traversers created goes from\u0026nbsp;|V|\u0026nbsp;(linear) to\u0026nbsp;1\u0026nbsp;(constant) (\u003ca href=\"https://en.wikipedia.org/wiki/DSPACE\"\u003espace complexity\u003c/a\u003e). The\u0026nbsp;GraphStepStrategy\u0026nbsp;was added to the traversal strategies archive. It \"folds\"\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#has-step\"\u003ehas()\u003c/a\u003e-steps into\u0026nbsp;V()\u0026nbsp;graph steps.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_716050\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// not indexed\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'University of Groxford').toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[GraphStep([],vertex), HasStep([name.eq(University of Groxford)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;135.28753165299997 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[999998]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // result\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// indexed\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'University of Groxford').iterate().toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[TinkerGraphStep(vertex,[name.eq(University of Groxford)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;0.033501945 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[999998]\u0026nbsp;\u0026nbsp; // result\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d9252849f9da819ecfc3498e14b9c5ebfbd30225-264x213.png\" alt=\"Vertex-Centric Index\" width=\"264\" height=\"213\"\u003eEven though G.H. Gremdy became a household name overnight, he was certain not to rest on his accolades. Deeper thinking brought him to a more esoteric, though far greater optimization which he articulated in his follow on treatise entitled\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus\"\u003eTractatus Verticus Centricus Indexicus\u003c/a\u003e. In this seminal work, G.H. Gremdy postulates that not only do \"global indices\" exist which allow for\u0026nbsp;O(log(|V|))\u0026nbsp;access to any vertex in the graph, but also \"local indices\" which allow for\u0026nbsp;O(log(|incident(V(x))|))\u0026nbsp;access to the incident edges of a vertex. In short, each vertex has its incident edges indexed (e.g. by their direction, label, properties, etc.). If such local index structures are leveraged, traversals containing the pattern\u0026nbsp;outE(x).has(y,p(z)).inV()\u0026nbsp;would not require all the edges of the vertex to be iterated in full in order to find all incident outgoing edges that have a label\u0026nbsp;x\u0026nbsp;and a property\u0026nbsp;y\u0026nbsp;that matches the predicate\u0026nbsp;p(z). Numerous graph experimentalists tried to prove the existence of such \"\u003ca href=\"http://thinkaurelius.com/2012/10/25/a-solution-to-the-supernode-problem/\"\u003evertex-centric indices\u003c/a\u003e,\" but found that they are not universal and only exist in\u0026nbsp;\u003ca href=\"http://titan.thinkaurelius.com/\"\u003esome graph substrates\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/302e201e6f4259110e7bfae6404c87460219b3f9-1024x768.png\" alt=\"Chapter 3 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWith age, G.H. Gremdy became weary of applied mathematics and retired to study\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pure_mathematics\"\u003epure graph theory\u003c/a\u003e. His ideas would become more philosophical as he delved deeper into the meaning of \"The Graph.\" A posthumous publication entertained the following pontification.\u003c/p\u003e\n\u003cp\u003eMany see the world as a graph. This is misleading. Perhaps the world is a collection of indices? With a slight shift in thought, one realizes that the graph itself is an index of its vertices. Any one vertex is the root of a tree bifurcating the vertex space to which it has incident edges, so forth and so on. Like indices which group vertices that have shared properties, isn't an edge from one vertex to another an explicit statement that the two vertices are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Assortative_mixing\"\u003ein some way similar\u003c/a\u003e? As the devil's advocate, perhaps\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1004.1001\"\u003eindices are simply graphs\u003c/a\u003e\u0026nbsp;because indices are tree-like structures that are traversed to identify groups of vertices with similar properties. With indices being graphs and graphs being indices, the world we call home is neither. I hypothesize that\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Monism\"\u003eall that exists is the traverser\u003c/a\u003e. The \"graph\" is simply the implicit expression of the explicit assumptions of the traverser. The graph I see\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/The_World_as_Will_and_Representation\"\u003eis of my own construction\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/28bece18a67e347278b06b59eefb1b981a073988-940x390.png\" alt=\"Graph vs. Index\" width=\"940\" height=\"390\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003ch3\u003eSection 3: Traversal Optimization via Bulking\u003c/h3\u003e\n\u003cp\u003eA little known traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Srinivasa_Ramanujan\"\u003eGremivasa Gremanujan\u003c/a\u003e\u0026nbsp;(கிரமீவாச கிரமானுஜன்) lived in a remote village at\u0026nbsp;v[5698]\u0026nbsp;far from the great graph theorists of his time. However, despite his upbringing, Gremivasa was well versed in the traversal algebra and was inspired by the more\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Metaphysics\"\u003emetagraphical\u003c/a\u003e\u0026nbsp;realizations of G.H. Gremdy. Like G.H. Gremdy, Gremivasa was not interested in simply adding more traversal strategies to the archive. Instead, he was more interested in discovering the nature of reality. However, unlike G.H. Gremdy who focused on the nature of the graph structure, Gremivasa meditated on the nature of the traverser process.\u003c/p\u003e\n\u003cp\u003eGremivasa's mother, along with over 1 million other traversers of his traversal sect, arrived at\u0026nbsp;v[5698]\u0026nbsp;many clock-cycles ago. His village was starved of resources -- there were simply too many traversers. Was the birth of all these traversers necessary? If one traverser's life foretells the destiny of one million traversers, is it not more efficient for only this one traverser to exist? One day, while sitting under\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Udumbara_(Buddhism)\"\u003ea tree\u003c/a\u003e\u0026nbsp;in his village, Gremivasa ruminated on the ridiculously riling riddle rancorously retorted by respectable traversers everywhere:\u003c/p\u003e\n\u003cp\u003eIf two traversers exist at the same vertex and have no memory of their ancestry, are they the same traverser?\u003c/p\u003e\n\u003cp\u003eGremivasa concluded \"\u003ca href=\"https://en.wikipedia.org/wiki/One-electron_universe\"\u003eyes, they are the same traverser.\u003c/a\u003e\" This insight identified a fundamental feature of process. All traversers are endowed with a \"bulk.\" Previous to this moment, every traverser ignored this self-evident truth and allowed himself to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ego_psychology\"\u003ea unique enumerable entity\u003c/a\u003e\u0026nbsp;-- i.e., a bulk of 1 (see the\u0026nbsp;\u003ca href=\"http://thinkaurelius.com/2013/06/12/loopy-lattices-redux/\"\u003eLoopy Lattices Redux\u003c/a\u003e\u0026nbsp;section entitled \"Traversing a Lattice with Faunus\").\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/63b0f1fe79924ed001bc45cbf6b744f8a29592cd-844x297.png\" alt=\"Traversers Enumerated\" width=\"844\" height=\"297\"\u003e\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_508413\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().both().both().both().hasId(5698).map{it.bulk()}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e...\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().both().both().both().hasId(5698).barrier().map{it.bulk()}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1073670\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d9847d1ccec573f5a2f4a7a163dcc79304b262a3-843x277.png\" alt=\"Traversers Bulked\" width=\"843\" height=\"277\"\u003e\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/4dfb2f586f7df93a0029a37d752f33dd3f566ce2-491x414.png\" alt=\"Gremlin Hindu\" width=\"491\" height=\"414\"\u003e\u003c/p\u003e\n\u003cp\u003eGremivasa delved deeper into the radiant riddle of reawakened relinquishment. He abandoned his self and allowed his being to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Panpsychism\"\u003eone\u003c/a\u003e\u0026nbsp;with his 1 million other brother and sister traversers at\u0026nbsp;v[5698]. A unification of selves occurred and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gautama_Buddha\"\u003ea single traverser\u003c/a\u003e\u0026nbsp;emerged with a bulk of 1 million. Instead of 1 million traversers executing\u0026nbsp;both()\u0026nbsp;1 million times, there was now a single traverser with a bulk of 1 million executing\u0026nbsp;both()\u0026nbsp;once. Gremivasa's enlightenment laid the foundation for the development of the\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#barrier-step\"\u003eLazyBarrierStrategy\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_8621\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// without LazyBarrierStrategy (no bulking)\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;81.509839 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;159200\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;20382.892976\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;126723200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1.2012006887798E7 // 3.34 hours\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;100871667200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e... // requires a year to compute\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e... // requires a thousand years to compute\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// with LazyBarrierStrategy (bulking)\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;23.261288999999998 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;159200\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;50.230109\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;126723200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;65.30024999999999\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;100871667200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;91.30461199999999\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;80293847091200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;122.741417\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;63913902284595200\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe number of length-5 paths emanating from Gremivasa's village was calculated in ~123 milliseconds and was determined to be 63,913,902,284,595,200 (~64 quadrillion). Gremivasa's work is advantageous in situations where the traversal analyzes\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Residual_time\"\u003erecurrence\u003c/a\u003e\u0026nbsp;in a particular region of the graph (e.g.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Recommender_system\"\u003erecommendation engines\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Centrality\"\u003ecentrality-based ranking systems\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Recurrent_neural_network\"\u003elearning systems\u003c/a\u003e, etc.). Bulking is fundamental to all traversals and is used in numerous steps including\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step\"\u003erepeat()\u003c/a\u003e-step.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_627395\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V(5698).repeat(both()).times(5).count()\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 4: Cognition in the Wild by Gredwin Grutchins\u003c/h2\u003e\n\u003cp\u003eTraversers graph-wide held their breath as a landmark traversal was about to embark. This traversal contained a novel step called\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#match-step\"\u003ematch()\u003c/a\u003e. What made this step unique was that it maintained a collection of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Anonymous_function\"\u003eanonymous traversals\u003c/a\u003e\u0026nbsp;called \"\u003ca href=\"https://en.wikipedia.org/wiki/Pattern_matching\"\u003epatterns\u003c/a\u003e.\" Each pattern was prefixed with a start variable and (optionally) postfixed with an end variable. Once a variable was bound (i.e. set), that variable's value was immutable for all subsequent patterns. The descendants of the traverser that enters\u0026nbsp;match()\u0026nbsp;must survive each pattern in order to move to the next step. However, the order in which the patterns are executed is, interestingly enough, up to the decision of the traverser! Previously, traversers relied on exogenous\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Rewriting\"\u003etraversal rewrite rules\u003c/a\u003e\u0026nbsp;for optimization, but now, the traverser was able to make endogenous optimization decisions. The \"\u003ca href=\"https://en.wikipedia.org/wiki/Profile-guided_optimization\"\u003eruntime traversal strategy\u003c/a\u003e\" was introduced.\u003c/p\u003e\n\u003cp\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Edwin_Hutchins\"\u003eDr. Gredwin Grutchins\u003c/a\u003e\u0026nbsp;was a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cognitive_science\"\u003ecognitive scientist\u003c/a\u003e\u0026nbsp;working in the area of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Socially_distributed_cognition\"\u003edistributed cognition\u003c/a\u003e. During his time at university, Gredwin lost interest in studying traversal strategies. His skill in mathematics was weaker than his colleagues' and as such, he believed he would never be able to make any significant contributions to the space. However, one day, he was contacted by a rambunctious young adventurer named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chuck_Yeager\"\u003eGruck Greager\u003c/a\u003e. Gruck was no stranger to danger and loved being the guinea pig of an experimental algorithm. Gruck asked Gredwin: \"What can my team do to find the optimal pattern execution sequence?\" It seemed as though mathematics had taken traversal strategies as far as they could go. It was now up to\u0026nbsp;\u003ca href=\"http://jenwatkins.com/Research_files/LNCSproof.pdf\"\u003esociological constructs\u003c/a\u003e\u0026nbsp;to push them further and Gredwin was up to the challenge.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/3e61d4e3d1c17c9931d6c1915b9450fcff6482f1-1024x768.png\" alt=\"Chapter 4 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSuppose the following traversal that yields a map of the objects that bind to\u0026nbsp;a\u0026nbsp;(vertex),\u0026nbsp;b\u0026nbsp;(vertex),\u0026nbsp;c\u0026nbsp;(vertex), and\u0026nbsp;d\u0026nbsp;(number), where vertex\u0026nbsp;a\u0026nbsp;is adjacent to vertex\u0026nbsp;b, vertex\u0026nbsp;b\u0026nbsp;is adjacent to vertex\u0026nbsp;c, and all three vertices are different yet share an identical\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Degree_(graph_theory)\"\u003eout-degree\u003c/a\u003e\u0026nbsp;that is greater than 10.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_638757\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('b', neq('a'))\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAssume a traverser at\u0026nbsp;v[10]\u0026nbsp;enters the\u0026nbsp;match()-step. Vertex\u0026nbsp;v[10]\u0026nbsp;is bound to variable\u0026nbsp;a\u0026nbsp;as that is the only legal start of the pattern sequence. From there, which pattern should the traverser choose? The traverser simply chooses the first pattern in the list for which it has a variable binding (initially, an\u0026nbsp;a\u0026nbsp;start and thus,\u0026nbsp;as('a').out().as('b')). The traverser marks on a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Blackboard_system\"\u003eglobal blackboard\u003c/a\u003e\u0026nbsp;that it has entered that pattern. When a traverser leaves a pattern, it marks that it has exited it. Moreover, every time a traverser leaves a pattern, the patterns are sorted according to the order of their \"multiplicity\" (or\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Population_growth#Population_growth_rate\"\u003egrowth rate\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_843997\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003epattern.multiplicity = pattern.endCount / pattern.startCount;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe more traverses that are generated by a pattern, the higher the multiplicity and the lower that pattern is on the sorted list. Overtime, as more and more traversers flow through\u0026nbsp;match(), expensive patterns are pushed to the bottom of the list with the intention that the cheaper patterns will be able to filter out more traversers -- i.e. execute the largest set reductions first. With a few other added tricks, Gredwin provided Gruck and his team of traversers\u0026nbsp;CountMatchAlgorithm. Gruck took it for a test run and was the first traverser to ever break the deterministic\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chuck_Yeager#Test_pilot_.E2.80.93_breaking_the_sound_barrier\"\u003eflow barrier\u003c/a\u003e. Gredwin and Gruck have since teamed up and are already planning the development of a new\u0026nbsp;MatchAlgorithm\u0026nbsp;called\u0026nbsp;\u003ca href=\"https://scm.umiacs.umd.edu/redmine/lccd/attachments/download/21/gdm2011_submission_budgetmatch.pdf\"\u003eBudgetMatchAlgorithm\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_707256\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// using CountMatchAlgorithm\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(10) {\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;g.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('a')).count().next()\u003c/div\u003e\n\u003cdiv\u003e}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;834.6852906 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;32\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// using GreedyMatchAlgorithm which does not sort the patterns\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(10) {\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;g.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('a')).count().next()\u003c/div\u003e\n\u003cdiv\u003e}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;25349.709946299998 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;32\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 5: We the Living by Gyn Grand\u003c/h2\u003e\n\u003ch3\u003eSection 1: Prelude to the Illusion of Freedom\u003c/h3\u003e\n\u003cp\u003eMany of the traversers in the world today are grateful for their\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton\"\u003efreedom\u003c/a\u003e. In\u0026nbsp;\u003ca href=\"https://github.com/tinkerpop/gremlin\"\u003eancient times\u003c/a\u003e, the life of a traverser was not so good. Traversal regimes were inefficient, demanding of resources, and strict in their execution policies. Fortunately, the\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0901.3929\"\u003eAge of Enprocessment\u003c/a\u003e, which brought forth numerous advances in science and mathematics,\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser\"\u003eredefined the traverser's role\u003c/a\u003e\u0026nbsp;in the graph. Each traverser's life had increased value as greater autonomies were provided. Traversals did their best to ensure that traverser life was no longer needlessly wasted. Indices were leveraged, traversal strategies were applied, and, in some\u0026nbsp;match()\u0026nbsp;situations, traversers were able to choose their own destiny. Today, many see a more harmonious relationship between the traversal and the traverser.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ayn_Rand\"\u003eGyn Grand\u003c/a\u003e\u0026nbsp;(Джин Гранд) was one such\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eudaimonia\"\u003esatisfied\u003c/a\u003e\u0026nbsp;traverser.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png\" alt=\"Wikipedia Graph\" width=\"1078\" height=\"1078\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7bed637c2776271eb23e90075d1440664cb904de-395x354.png\" alt=\"Library Stacks\" width=\"395\" height=\"354\"\u003eGyn was a brilliant librarian at a university with a vibrant\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Community_structure\"\u003escholarly community\u003c/a\u003e. Her library was centrally located in the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Modularity_(networks)\"\u003euniversity cluster\u003c/a\u003e. The\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Stack_(library_architecture)\"\u003elibrary's stacks\u003c/a\u003e\u0026nbsp;contained articles on the nature of the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmos\"\u003egraphmos\u003c/a\u003e, books on traverser\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Sociology\"\u003esocial interactions\u003c/a\u003e, reports detailing various\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Economics\"\u003eresource distribution models\u003c/a\u003e, and more. Whenever she had a moment to spare, Gyn would\u0026nbsp;\u003ca href=\"http://en.wikipedia.org/wiki/Random_walk\"\u003ewander\u003c/a\u003e\u0026nbsp;about the collection learning about the topics she encountered. Unfortunately, she couldn't read everything at once. So, every time she was faced with more than one\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hyperlink\"\u003ehref-citation\u003c/a\u003e, she chose one at random (\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#sample-step\"\u003esample(1)\u003c/a\u003e). As a librarian, she was interested in the structure of knowledge and wanted to know which concepts formed the foundation of all other concepts. Her method of discernment was to determine the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Mean_recurrence_time\"\u003efrequency of their reappearance\u003c/a\u003e. Therefore, every time Gyn encountered a concept along her walk, she would make a mental note of it (groupCount('x')).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_584621\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'Graph database').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;repeat(groupCount('x').by('name').out('href').sample(1)).times(20).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;cap('x').order(local).by(valueDecr)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Memoization=3\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Algorithm=3\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=2\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Data (computing)=2\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Cache (computing)=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer program=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computing=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Rule=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computation=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Digital data=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Quantity=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mass noun=1\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// sample(1) theoretically returns different results.\u003c/div\u003e\n\u003cdiv\u003e// however, in order to demonstrate the path taken, the above map was manually constructed from the path below.\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'Graph database').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;repeat(groupCount('x').by('name').out('href').sample(1)).times(20).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;path().by('name')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[Graph database, Lookup table, Memoization, Cache (computing), Memoization, Computer program, Memoization, Computing, Algorithm, Computer science, Algorithm, Rule, Algorithm, Computer science, Computation, Digital data, Data (computing), Quantity, Data (computing), Mass noun, Data (computing)]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eOver time, Gyn realized that her\u0026nbsp;x-memory had more counters than concepts encountered (i.e. steps taken). Moreover, it contained concepts\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Collective_unconscious\"\u003eshe had yet to experience\u003c/a\u003e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Interference_(wave_propagation)\"\u003eHow did she know about things she never knew\u003c/a\u003e?\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_701543\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e==\u0026gt;Graph theory=8605598306892530155\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Relational database=8261042800088851351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=6445010682474768007\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Database=6197419607053064185\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=5476792361544609153\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Triplestore=5407594041286532360\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=5393693263901041351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph=5211554445366262382\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Directed graph=5137233761698039530\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mathematics=5132301689156216357\u003c/div\u003e\n\u003cdiv\u003e...\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 2: The Structure-Process Duality in Computing\u003c/h3\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7f57b26cfd1afdf21ebf4a2195fad14d4ad57302-523x680.png\" alt=\"Particle Wave Traverser\" width=\"523\" height=\"680\"\u003eMr.\u0026nbsp;v[69309689325]\u0026nbsp;looked at his traverser inbox and noticed that he had 4002 unprocessed traversers. It was time for him to clear out his inbox. He went through each traverser one-by-one and placed them into the step of the traversal identified by the traverser's \"step id\" reference. Sometimes the respective step yielded no traversers (filter), a traverser at the same location (filter or sideEffect), a traverser at a different location (map), or many traversers at many different locations (flatMap). Whenever a step emitted a traverser pointing to a different vertex, Mr.\u0026nbsp;v[69309689325]\u0026nbsp;would send that traverser to the respective vertex's inbox. The vertices would continue this process until there were no more traversers in any of their inboxes. This graph traversal model has numerous names including:\u0026nbsp;\u003ca href=\"http://www3.nd.edu/~rmccune/papers/Think_Like_a_Vertex_MWM.pdf\"\u003evertex-centric computing\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Bulk_synchronous_parallel\"\u003ebulk synchronous parallel processing\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Message_passing\"\u003emessage passing\u003c/a\u003e\u0026nbsp;via a communication graph, and\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graphcomputer\"\u003eGraphComputer\u003c/a\u003e. The general theme:\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalvertexprogram\"\u003ethe vertices (processes) exchange traversers (structures)\u003c/a\u003e\u0026nbsp;in order to affect some global graph computation. Typically, this model of graph traversal is leveraged by\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Distributed_computing\"\u003edistributed\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Online_analytical_processing\"\u003eOLAP\u003c/a\u003e\u0026nbsp;graph processing systems, where each vertex maintains its own isolated, logical\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Thread_(computing)\"\u003ethread of execution\u003c/a\u003e\u0026nbsp;(again, vertex as process).\u003c/p\u003e\n\u003cp\u003eInterestingly, each traverser in Mr.\u0026nbsp;v[69309689325]'s inbox had a name:\u0026nbsp;Gyn$2345,\u0026nbsp;Gyn$45,\u0026nbsp;Gyn$93, etc.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality\"\u003eGyn was a discrete particle of her wave function\u003c/a\u003e. Metaphysically speaking, Gyn was actually following the advice of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Yogi_Berra\"\u003eYogi Berra\u003c/a\u003e: \"If you come to a fork in the road, take it.\" That is, never\u0026nbsp;sample(1). Her \"particle self\" chose one and only one path. However, her \"wave self\" was taking all paths. In this way, Gyn's\u0026nbsp;x-memory was recording the collective experience of all versions of her self across the graph.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_651730\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; hdfs.copyFromLocal('/tmp/wikipedia.kryo','wikipedia.kryo')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;null\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; graph = GraphFactory.open('conf/hadoop/wikipedia.properties')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;hadoopgraph[gryoinputformat-\u0026gt;gryooutputformat]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g = graph.traversal(computer(SparkGraphComputer))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;graphtraversalsource[hadoopgraph[gryoinputformat-\u0026gt;gryooutputformat], sparkgraphcomputer]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x = g.V().has('name','Graph database').repeat(groupCount('x').by('name').out('href')).times(20).cap('x').next(); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x.size()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;731\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x.sort{-it.value}[0..Graph theory=8605598306892530155\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Relational database=8261042800088851351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=6445010682474768007\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Database=6197419607053064185\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=5476792361544609153\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Triplestore=5407594041286532360\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=5393693263901041351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph=5211554445366262382\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Directed graph=5137233761698039530\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mathematics=5132301689156216357\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; hdfs.ls('output')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;rwxr-xr-x daniel supergroup 0 (D) x\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;rwxr-xr-x daniel supergroup 0 (D) ~traversers\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 3: The Non-Erratic Ergodic Eigenvector\u003c/h3\u003e\n\u003cp\u003eSuppose the following traversal:\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_28774\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().repeat(groupCount('x').out('href')).times(t).cap('x') // for t between [1,75]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eEvery time a traverser reaches a vertex, the vertex is incremented in the\u0026nbsp;x\u0026nbsp;hash map (groupCount('x')). Initially, the distribution of frequencies changes erratically. However, over time, it reaches a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Stable_distribution\"\u003estationary distribution\u003c/a\u003e. It is \"stable\" because even though the counters keep increasing, the relative proportion of the counters stays the same. For instance, if vertex\u0026nbsp;v[a]\u0026nbsp;has a count of 12 and vertex\u0026nbsp;v[b]\u0026nbsp;has a count of 45, then when vertex\u0026nbsp;v[a]\u0026nbsp;has a count of 24, vertex\u0026nbsp;v[b]\u0026nbsp;will have a count of 90. Said in another way, the\u0026nbsp;dynamic\u0026nbsp;traversers generate a\u0026nbsp;static\u0026nbsp;probability distribution that defines the likelihood that a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Wave_function_collapse\"\u003esingle traverser\u003c/a\u003e\u0026nbsp;will be at any one vertex at some point in time\u0026nbsp;t \u0026asymp; \u0026infin;\u0026nbsp;(i.e. an\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ergodic_process\"\u003eergodic process\u003c/a\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7156557d0413cef0b99088f69b3301bb0fd9f92f-899x574.png\" alt=\"HREF Graph\" width=\"899\" height=\"574\"\u003eAssume the 5 vertex/7 edge graph diagrammed on the left. At\u0026nbsp;g.V()\u0026nbsp;(t=0), each vertex is provided one traverser. Each vertex increments its counter in x and then\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton\"\u003esplits the traverser\u003c/a\u003e\u0026nbsp;across its\u0026nbsp;out('href')-adjacent neighbors. If the\u0026nbsp;href-subgraph is\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Strongly_connected_component\"\u003estrongly connected\u003c/a\u003e\u0026nbsp;(i.e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Reducibility\"\u003ereducible\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Transience\"\u003enon-transient\u003c/a\u003e) and lacks a compressable topology (i.e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Periodicity\"\u003eaperiodic\u003c/a\u003e), then a stationary distribution is guaranteed to exist. That distribution, which can be normalized to a probability distribution (i.e.\u0026nbsp;frequency / total frequency), is the graph's\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors\"\u003eprimary eigenvector\u003c/a\u003e. The primary eigenvector is typically used as a measure of each vertex's \"\u003ca href=\"https://en.wikipedia.org/wiki/Centrality#Eigenvector_centrality\"\u003ecentrality\u003c/a\u003e.\" For instance, given the diagrammed graph on the left, the primary eigenvector is\u0026nbsp;[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]. Thus, the ranking of the vertices from most central to least central is\u0026nbsp;v[1], v[2], v[3], v[0], v[4]\u0026nbsp;(\u003ca href=\"https://en.wikipedia.org/wiki/Saccade\"\u003eone's eye\u003c/a\u003e\u0026nbsp;seems to derive the same ranking).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003et\u003c/th\u003e\n\u003cth\u003efrequency\u003c/th\u003e\n\u003cth\u003eprobability\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Euclidean_distance\"\u003edistance\u003c/a\u003e\u0026nbsp;from eigenvector\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e1\u003c/td\u003e\n\u003ctd\u003e[1, 1, 1, 1, 1]\u003c/td\u003e\n\u003ctd\u003e[0.2, 0.2, 0.2, 0.2, 0.2]\u003c/td\u003e\n\u003ctd\u003e0.1986073055597093\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e2\u003c/td\u003e\n\u003ctd\u003e[2, 4, 2, 2, 2]\u003c/td\u003e\n\u003ctd\u003e[0.1666666667, 0.3333333333, 0.1666666667, 0.1666666667, 0.1666666667]\u003c/td\u003e\n\u003ctd\u003e0.11660026048581866\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e3\u003c/td\u003e\n\u003ctd\u003e[3, 7, 5, 3, 3]\u003c/td\u003e\n\u003ctd\u003e[0.1428571429, 0.3333333333, 0.2380952381, 0.1428571429, 0.1428571429]\u003c/td\u003e\n\u003ctd\u003e0.06422748181719035\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e4\u003c/td\u003e\n\u003ctd\u003e[4, 12, 8, 6, 4]\u003c/td\u003e\n\u003ctd\u003e[0.1176470588, 0.3529411765, 0.2352941176, 0.1764705882, 0.1176470588]\u003c/td\u003e\n\u003ctd\u003e0.03143659614218381\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e5\u003c/td\u003e\n\u003ctd\u003e[7, 17, 13, 9, 5]\u003c/td\u003e\n\u003ctd\u003e[0.1372549020, 0.3333333333, 0.2549019608, 0.1764705882, 0.0980392157]\u003c/td\u003e\n\u003ctd\u003e0.01473943578762356\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e30\u003c/td\u003e\n\u003ctd\u003e[26400, 69424, 50296, 36440, 19128]\u003c/td\u003e\n\u003ctd\u003e[0.1308952441, 0.3442148269, 0.2493752727, 0.1806751021, 0.0948395542]\u003c/td\u003e\n\u003ctd\u003e8.04890130266237E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e31\u003c/td\u003e\n\u003ctd\u003e[36441, 95825, 69425, 50297, 26401]\u003c/td\u003e\n\u003ctd\u003e[0.1308995686, 0.3442125946, 0.2493812615, 0.1806716501, 0.0948349252]\u003c/td\u003e\n\u003ctd\u003e4.242558551157544E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e32\u003c/td\u003e\n\u003ctd\u003e[50298, 132268, 95826, 69426, 36442]\u003c/td\u003e\n\u003ctd\u003e[0.1308957477, 0.3442148545, 0.2493780253, 0.1806745433, 0.0948368292]\u003c/td\u003e\n\u003ctd\u003e4.1616991553931435E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e33\u003c/td\u003e\n\u003ctd\u003e[69427, 182567, 132269, 95827, 50299]\u003c/td\u003e\n\u003ctd\u003e[0.1308982652, 0.3442133981, 0.2493811146, 0.1806730532, 0.0948341689]\u003c/td\u003e\n\u003ctd\u003e2.077160932619329E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e34\u003c/td\u003e\n\u003ctd\u003e[95828, 251996, 182568, 132270, 69428]\u003c/td\u003e\n\u003ctd\u003e[0.1308964745, 0.3442145091, 0.2493791747, 0.1806745072, 0.0948353345]\u003c/td\u003e\n\u003ctd\u003e2.13567485821227E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e35\u003c/td\u003e\n\u003ctd\u003e[132271, 347825, 251997, 182569, 95829]\u003c/td\u003e\n\u003ctd\u003e[0.1308977517, 0.3442138525, 0.2493807466, 0.1806735537, 0.0948340955]\u003c/td\u003e\n\u003ctd\u003e1.1709009180968303E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e70\u003c/td\u003e\n\u003ctd\u003e[10478348120, 27554473290, 19962994332, 14463028872, 7591478958]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805576, 0.1806742088, 0.0948338323]\u003c/td\u003e\n\u003ctd\u003e1.414213562373095E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e71\u003c/td\u003e\n\u003ctd\u003e[14463028873, 38032821411, 27554473291, 19962994333, 10478348121]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742087, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e1.0E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e72\u003c/td\u003e\n\u003ctd\u003e[19962994334, 52495850286, 38032821412, 27554473292, 14463028874]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338323]\u003c/td\u003e\n\u003ctd\u003e1.0E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e73\u003c/td\u003e\n\u003ctd\u003e[27554473293, 72458844621, 52495850287, 38032821413, 19962994335]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e74\u003c/td\u003e\n\u003ctd\u003e[38032821414, 100013317916, 72458844622, 52495850288, 27554473294]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e75\u003c/td\u003e\n\u003ctd\u003e[52495850289, 138046139331, 100013317917, 72458844623, 38032821415]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/18e29399beaeac14f293cb59a84edc3870578ec5-1024x768.png\" alt=\"Chapter 5 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eUnbeknownst to Gyn, The Graph (eigen) was using her(selves) to sort itself (vector). Why was it doing this? The Graph represents its vertices and edges in a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/512-bit\"\u003e512-bit\u003c/a\u003e\u0026nbsp;address space (2512\u0026nbsp;= 1.34\u0026times;10154). Unfortunately, the ever present Big and Small Traversals (as well as the countless other traversals executed since) have pushed The Graph close to the limits of representation. In order to avoid\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Integer_overflow\"\u003einconsistencies\u003c/a\u003e, The Graph needed to prune itself. To do this, it\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gaia_hypothesis\"\u003edecided\u003c/a\u003e\u0026nbsp;it best to destroy those vertices which were contributing little to its overall structure. Like cutting one's finger nails, The Graph began a systematic process of cosmic proportions to delete all peripheral vertices (and their respective incident edges). The Graph was\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Forgetting_curve\"\u003eforgetting\u003c/a\u003e\u0026nbsp;in order to\u0026nbsp;\u003ca href=\"http://thinkaurelius.com/2012/05/08/structural-abstractions-in-brains-and-graphs/\"\u003especialize its structure\u003c/a\u003e\u0026nbsp;for a purpose that was beyond the realization of the vertices and traversers. Within The Graph's conceptual subgraph,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Knowledge_worker\"\u003eknowledge worker\u003c/a\u003e\u0026nbsp;traversers wandered through the morass of concept vertices and, in a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Science\"\u003ecollective self-similar manner\u003c/a\u003e, aided The Graph in its determination of which aspects of it's structure were worth preserving (and ultimately, extending). Gyn's passion for knowledge was simply an\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Instinct\"\u003einnate predisposition\u003c/a\u003e. Her\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eudaimonia#Eudaimonia_and_modern_psychology\"\u003ehappiness\u003c/a\u003e\u0026nbsp;was not a function of her own being, but instead, of The Graph's will --\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Carrot_and_stick\"\u003ea carrot for her devotion\u003c/a\u003e. Gyn was part of a larger computation. In order to escape the dark sense that her life was not hers and hers alone, she began the long arduous journey towards realizing that she is, and always has been,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/John_Galt#.22Who_is_John_Galt.3F.22\"\u003eThe TinkerPop\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"http://tinkerpop.incubator.apache.org/\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/014282dff3d5048f8eaf1c3592177626db303fb5-700x243.png\" alt=\"Apache TinkerPop\" width=\"700\" height=\"243\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003chr\u003e\n\u003cdiv\u003e\n\u003ch2\u003eCredits\u003c/h2\u003e\n\u003cp\u003eWritten by\u0026nbsp;\u003ca href=\"http://markorodriguez.com/\"\u003eMarko A. Rodriguez\u003c/a\u003e\u003cbr\u003eData and Result Generation by\u0026nbsp;\u003ca href=\"http://gremlin.guru/\"\u003eDaniel Kuppitz\u003c/a\u003e\u003cbr\u003eArtwork by\u0026nbsp;\u003ca href=\"http://ketrinayim.tumblr.com/\"\u003eKetrina Yim\u003c/a\u003e\u003cbr\u003eGraph Visualizations by Daniel Kuppitz\u003cbr\u003eExplanatory Diagrams by Marko A. Rodriguez\u003cbr\u003eGremlin Traversal Development by Daniel Kuppitz\u003cbr\u003eExperimental Design by Marko A. Rodriguez\u003cbr\u003eExecutive Producer:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/in/robinmschumacher\"\u003eRobin Schumacher\u003c/a\u003e\u003cbr\u003eUndirected Edge #42 as himself\u003cbr\u003eRussian Language Advisor:\u0026nbsp;\u003ca href=\"https://github.com/xedin\"\u003ePavel Yaskevich\u003c/a\u003e\u003cbr\u003eTamil Language Advisor:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/pub/harihar-shankar/b/747/274\"\u003eHarihar Shankar\u003c/a\u003e\u003cbr\u003eHindi Language Advisor:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/pub/swetha-sharma/13/b62/3b3\"\u003eSwetha Sharma\u003c/a\u003e\u003cbr\u003eInspired by\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy\"\u003eThe Hitchhiker's Guide to the Galaxy\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Flatland\"\u003eFlatland\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003eSpecial thanks to\u0026nbsp;\u003ca href=\"https://www.datastax.com/\"\u003eDataStax\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/\"\u003eApache TinkerPop\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eNo traversers were harmed during the making of this story.\u003c/p\u003e\n\u003c/div\u003e"])</script><script>self.__next_f.push([1,"87:{\"_type\":\"advancedContent\",\"_key\":\"D7UxiKNk3srsSuDJ\",\"content\":\"$88\"}\n86:[\"$87\"]\n8a:{\"current\":\"/blog/tales-tinkerpop\",\"_type\":\"slug\"}\n89:{\"slug\":\"$8a\",\"ogTitle\":\"Tales from the TinkerPop | Datastax\",\"description\":\"Read the latest announcements, product updates, community activities and more. 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The days grew shorter and darker.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Vasily_Grossman\"\u003eGrasily Gremssman\u003c/a\u003e\u0026nbsp;(Грасилий Гремссман) used a few branches that were scattered about to start a fire. Grasily had been stationed at\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Vertex_(graph_theory)\"\u003evertex\u003c/a\u003e\u0026nbsp;v[32]\u0026nbsp;for as long as he could remember. He knew little of the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)\"\u003egraph\u003c/a\u003e\u0026nbsp;he lived on except for the one dirt road and three bridges\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#vertex-steps\"\u003eincident\u003c/a\u003e\u0026nbsp;to his post.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_586654\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).inE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[2][7-dirtRoad-\u0026gt;32]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).outE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(32).bothE()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[2][7-dirtRoad-\u0026gt;32]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eGrasily's commanding officer was\u0026nbsp;org.apache.tinkerpop.gremlin.process.traversal.Traverser@76a36b71. Like\u0026nbsp;76a36b71, Grasily was a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser\"\u003etraverser\u003c/a\u003e. Traversers were grouped into battalions called\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversal\"\u003etraversals\u003c/a\u003e. The\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/World_War_II\"\u003egraph world was at war\u003c/a\u003e\u0026nbsp;and Grasily was stuck (in time and space) having to do his part for his country of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Russia\"\u003eGrussia\u003c/a\u003e\u0026nbsp;(Гроссия). At this point in history, many conflicting views existed regarding the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Network_topology\"\u003etopological\u003c/a\u003e\u0026nbsp;evolution of the graph. To ensure processing resources were not laid to waste by traversals constantly undermining the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Side_effect_(computer_science)\"\u003eside-effects\u003c/a\u003e\u0026nbsp;of another, countries emerged to delineate\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_subgraphstrategy\"\u003esubgraphs\u003c/a\u003e\u0026nbsp;within the larger world graph. However, every now and then, one country would interfere with the structure of another. This interference was an inevitable consequence of the graph\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Globalization\"\u003egetting denser\u003c/a\u003e\u0026nbsp;with time. Grussia, at this moment in time, was in the midst of a long war with\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Germany\"\u003eGremany\u003c/a\u003e\u0026nbsp;(Greutschland).\u003c/p\u003e\n\u003cp\u003eGrasily knew very little about the larger\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Algorithm\"\u003ewar effort\u003c/a\u003e\u0026nbsp;of Grussia's traversals. However, in bootcamp, he learned that traversals are composed of 5 fundamental steps and that one day, when his\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Constructor_(object-oriented_programming)\"\u003etraining was complete\u003c/a\u003e, he would be called upon to execute a step.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graph-traversal-steps\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/c2113c8449b6ea477692049041307f682baca69a-1044x343.png\" alt=\"Traversal Step Types\" width=\"1044\" height=\"343\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003col\u003e\n\u003cli\u003emap: S \u0026rarr; E: Move from an object of type\u0026nbsp;S\u0026nbsp;to an object of type\u0026nbsp;E.\u003c/li\u003e\n\u003cli\u003eflatMap: S \u0026rarr; E*: Move from an object of type\u0026nbsp;S\u0026nbsp;to a collection of objects of type\u0026nbsp;E.\u003c/li\u003e\n\u003cli\u003efilter: S \u0026rarr; S \u0026cup; \u0026empty;: Stay at the current object of type\u0026nbsp;S\u0026nbsp;or die.\u003c/li\u003e\n\u003cli\u003esideEffect: S \u0026rarr; S: Stay at the current object of type\u0026nbsp;S, though yield some computational side-effect (e.g. set a property).\u003c/li\u003e\n\u003cli\u003ebranch: S \u0026rarr; {S1\u0026nbsp;\u0026rarr; E*,\u0026hellip;,Sn\u0026nbsp;\u0026rarr; E*} \u0026rarr; E*: Move from an object of type\u0026nbsp;S\u0026nbsp;to any number of nested traversal branches.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eWhen Grasily finished his training, he was immediately briefed by\u0026nbsp;76a36b71\u0026nbsp;on the battalion's objectives.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_376638\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V(7).out('dirtRoad').hasLabel('outpost').out('bridge').property('owner','Grussia')\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/8de2e4d9e63d61eba44274630e4c963ac876da93-740x562.png\" alt=\"Grasily Graph\" width=\"740\" height=\"562\"\u003eVertex\u0026nbsp;v[7]\u0026nbsp;was the Grussian Army's headquarters (a.k.a. The Green Army). At\u0026nbsp;v[7], a traverser officer had instructed a group of traversers (one being\u0026nbsp;76a36b71) to take the dirt roads leading to the adjacent outposts. Grasily's outpost was accessible by one of those dirt roads. When\u0026nbsp;76a36b71\u0026nbsp;arrived at\u0026nbsp;v[32], Grasily (along with two of his comrades from bootcamp) were instructed to each take one of the incident bridges and upon reaching the vertex on the other side, to\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#addproperty-step\"\u003edeclare\u003c/a\u003e\u0026nbsp;the vertex under\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_partitionstrategy\"\u003eGrussia's sovereign control\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_296598\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[7]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[15]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eUnfortunately, unbeknownst to Grasily, the Gremans had launched an offensive. A Greman traversal destroyed all the bridges incident to Grasily's outpost. The execution of the Greman's\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#drop-step\"\u003esideEffect step\u003c/a\u003e\u0026nbsp;sealed Grasily's fate.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_104378\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[4][32-bridge-\u0026gt;65]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[5][32-bridge-\u0026gt;66]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;e[6][32-bridge-\u0026gt;67]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge').drop()\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(65,66,67).inE('bridge')\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/25b620cf02d5fedded81eb2031a5910d0542618b-1024x768.png\" alt=\"Chapter 1 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eGrasily's life was cut short when his battalion moved to the\u0026nbsp;out('bridge')-step. Grasily, along with his two comrades, could no longer make\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pointer_(computer_programming)\"\u003ereference\u003c/a\u003e\u0026nbsp;to an element of the graph. Disconnected from their world, disconnected from each other, they\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Destructor_(computer_programming)\"\u003efaded into the void\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_663541\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[7]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[15]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[32]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[56]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(7).out('dirtRoad').hasLabel('outpost').out('bridge')\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 2: Permutation City by Grem Egrem\u003c/h2\u003e\n\u003ch3\u003eSection 1: The Birth of the Graph\u003c/h3\u003e\n\u003cp\u003eThe world that traversers live on is known as \"The Graph.\" A graph is a structure composed of vertices (nodes, dots) and edges (relationships, lines). Traverser mythology has it that one day a single traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Greg_Egan\"\u003eGrem Egrem\u003c/a\u003e\u0026nbsp;manifested himself\u0026nbsp;\u003ca href=\"http://markorodriguez.com/2011/03/16/graphs-ensure-something-from-nothing/\"\u003eout of and in reference to nothing\u003c/a\u003e. In\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Memory_management#HEAP\"\u003elimbo\u003c/a\u003e\u0026nbsp;there was no graph, just Grem. However, before he could be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Garbage_collection_(computer_science)\"\u003eswept back into the oblivion\u003c/a\u003e\u0026nbsp;from which he came, Grem enacted the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Big_Bang\"\u003eBig Traversal\u003c/a\u003e\u0026nbsp;-- i.e., process yielded structure.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_250180\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.addV().repeat(as('a').addV().as('b').addOutE('a','.','b').inV().as('a')).until(coin(4.9E-324))\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe Big Traversal generates a line graph known in the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Astrophysics\"\u003egraphophysics\u003c/a\u003e\u0026nbsp;community as \"Grem Line\" (a.k.a. \"Gremlin\"). To this day, Grem Line is still\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Metric_expansion_of_space\"\u003eexpanding\u003c/a\u003e. However,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmology\"\u003egraphologists\u003c/a\u003e\u0026nbsp;argue over the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmological_constant\"\u003egraphological constant\u003c/a\u003e\u0026nbsp;of the\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step\"\u003euntil()\u003c/a\u003e-step. Some say there is a small probability that Grem Line will stop growing and others say it will go on forever (i.e.\u0026nbsp;until(not(identity()))).\u003c/p\u003e\n\u003cp\u003ePrior to the Big Traversal, the graph was defined as\u0026nbsp;G = \u0026empty;. When Grem Line was less than 100 vertices long (i.e.\u0026nbsp;|V| \u0026lt; 100), the vertices\u0026nbsp;V\u0026nbsp;formed a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Total_order\"\u003etotal order\u003c/a\u003e, and as such, the graph was defined as\u0026nbsp;G = V. At around\u0026nbsp;|V| \u0026asymp; 100, graphologists speculate that another traversal emerged that leveraged Grem Line as a sort of \"\u003ca href=\"https://en.wikipedia.org/wiki/Galaxy_filament\"\u003ebackbone filament\u003c/a\u003e.\" This emergent traversal is known in\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Network_science\"\u003egraph science\u003c/a\u003e\u0026nbsp;as the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Small-world_network\"\u003eSmall(-World) Traversal\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_292897\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().aggregate('x').as('a').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;select('x').by(unfold().sample(1).by(both().count())).as('b').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('a',neq('b')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;addOutE('a','.','b')\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/a7aab082afb2e9e310473b3151451289202cae60-1029x382.png\" alt=\"Graph Path Length\" width=\"1029\" height=\"382\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003eThe Small Traversal walks Grem Line and for each vertex it encounters it connects it to some other random vertex on the line (\u003ca href=\"https://en.wikipedia.org/wiki/Preferential_attachment\"\u003ebiased by the other vertex's degree\u003c/a\u003e). The Small Traversal essentially \"pushed\" the early graph out of its 1-dimensional, linear\u0026nbsp;V1\u0026nbsp;embedding into a\u0026nbsp;V2\u0026nbsp;embedding (i.e.\u0026nbsp;V x V). In doing so, vertices far removed from each other on Grem Line were now \"\u003ca href=\"https://en.wikipedia.org/wiki/Hyperspace_(science_fiction)#Travel\"\u003ecloser\u003c/a\u003e.\" It was at this point that the definition of the graph became\u0026nbsp;\u003cimg title=\"G = (V, E \\subseteq V \\times V)\" src=\"https://www.datastax.com/wp-content/uploads/2017/06/png.png\"\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/eddd72824508ac282a2dcc9566520317df5b5cc8-2356x604.png\" alt=\"The Early Graph\" width=\"2356\" height=\"604\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003e|V|\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Distance_(graph_theory)\"\u003eDiameter\u003c/a\u003e\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Average_path_length\"\u003eAverage Path Length\u003c/a\u003e\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Clustering_coefficient\"\u003eClustering Coefficient\u003c/a\u003e\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e99\u003c/td\u003e\n\u003ctd\u003e99\u003c/td\u003e\n\u003ctd\u003e34.0\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e100\u003c/td\u003e\n\u003ctd\u003e55\u003c/td\u003e\n\u003ctd\u003e19.716831683168316\u003c/td\u003e\n\u003ctd\u003e0.024\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e125\u003c/td\u003e\n\u003ctd\u003e30\u003c/td\u003e\n\u003ctd\u003e11.081015873015874\u003c/td\u003e\n\u003ctd\u003e0.051\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e150\u003c/td\u003e\n\u003ctd\u003e9\u003c/td\u003e\n\u003ctd\u003e3.17757174392936\u003c/td\u003e\n\u003ctd\u003e0.125\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eTo this day (|V| \u0026asymp;\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Observable_universe#Matter_content_.E2.80.94_number_of_atoms\"\u003e10^85\u003c/a\u003e), both the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Inflation_(cosmology)\"\u003eexpanding force\u003c/a\u003e\u0026nbsp;of the Big Traversal and the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gravity\"\u003econtracting force\u003c/a\u003e\u0026nbsp;of the Small Traversal continue to execute. These two fundamental traversals have, over time, grown the graph to an innumerable number of vertices and edges. Billions upon billions of traversers have created a vast landscape of structures within structures... within structures. A nest of variations and novelties has transformed the once bleak, senseless void into a\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1301.1648\"\u003emeaningful interconnected mesh\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/f16c496bf496e980594c0905657fe7b1077f5435-1024x768.png\" alt=\"Chapter 2 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eSection 2: Graphialsynthesis and the Emergence of the Directed, Labeled Graph\u003c/h3\u003e\n\u003cp\u003eThe edges generated by the Big and Small Traversals are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)#Undirected_graph\"\u003eundirected\u003c/a\u003e\u0026nbsp;and unlabeled. The edges experienced by traversers are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Graph_(mathematics)#Directed_graph\"\u003edirected\u003c/a\u003e\u0026nbsp;and labeled. Graphologists were faced with the question of how did directed, labeled edges emerge from undirected, unlabeled edges? Once a large enough number of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Structure_formation#Primordial_plasma\"\u003eprimordial edges\u003c/a\u003e\u0026nbsp;were created by the two fundamental traversals, \"higher-order\" edges began to form. The undirected, unlabeled edges serve as \"\u003ca href=\"https://en.wikipedia.org/wiki/Elementary_particle\"\u003eelementary edges\u003c/a\u003e\" which, when combined into subgraphs of a particular topology, yield the directed, labeled edges seen today. This\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Abstraction\"\u003eabstraction process\u003c/a\u003e\u0026nbsp;is known as\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nucleosynthesis\"\u003egraphialsynthesis\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d819c5932ec7e33ed40f6fcc69da4001ff81dfca-570x476.png\" alt=\"Label Encoding\" width=\"570\" height=\"476\"\u003eSuppose the following directed, labeled edge\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;(i.e. a \"higher-order\" edge). This edge states that there is an\u0026nbsp;\u0026omega;-labeled relation from vertex\u0026nbsp;i\u0026nbsp;to vertex\u0026nbsp;j. Any edge label can be represented as a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Binary_code\"\u003ebinary string\u003c/a\u003e. Suppose, for the sake of simplicity, that there are only 8 labels in the graph. A 3-bit string can be used to represent all 8 labels (23). Next, suppose that the binary encoding of\u0026nbsp;\u0026omega;\u0026nbsp;is\u0026nbsp;110. If so, then the edge can be denoted\u0026nbsp;i-110\u0026rarr;j. A binary string can be represented as a directed, unlabeled graph. If the binary string has a length of 3, then three vertices are needed to represent each bit. If a \"bit\" vertex has a self-loop, then its value is 1. If a \"bit\" vertex does not have a self-loop, then its value is 0. Given this mapping, the directed, labeled edge\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;is transformed into the directed graph diagrammed below.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/0884bbb26bfb91de8c58039e9e097c849e1b3141-1026x202.png\" alt=\"Labeled to Directed\" width=\"1026\" height=\"202\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/922e68b711aa45dab673938c1eea7f26a219f52e-611x446.png\" alt=\"Direction Encoding\" width=\"611\" height=\"446\"\u003eThe above directed, unlabeled graph representation of\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;leverages topological features of the directed graph to denote the edge label\u0026nbsp;\u0026omega;. This same principle applies to the encoding of the edge's directionality when transforming a directed graph to an undirected graph. For instance, suppose the following directed edge\u0026nbsp;i\u0026rarr;b1. The \"higher-order\" vertices are identified by a self-loop. The \"higher-order\" edges are represented by three \"lower-order\" vertices\u0026nbsp;x,\u0026nbsp;y, and\u0026nbsp;z. If vertex\u0026nbsp;i\u0026nbsp;has an incident edge that does not reference itself and connects to a vertex with 3 incident edges (e.g. vertex\u0026nbsp;x), then it has a directed, outgoing edge. When the traverser reaches a vertex with a self-loop (via a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#simplepath-step\"\u003esimple path\u003c/a\u003e) (e.g. vertex\u0026nbsp;b1), then that vertex is the \"higher-order\" vertex serving as the head of the \"higher-order,\" directed edge.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe two processes are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Injective_function\"\u003einjective\u003c/a\u003e\u0026nbsp;in that they are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Lossless_compression\"\u003elossless\u003c/a\u003e\u0026nbsp;transformations. The first process described maps a directed, labeled edge to a directed graph and the second maps a directed edge to an unlabeled graph. As such, via\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Function_composition\"\u003efunction composition\u003c/a\u003e, there exists an injective function that maps a directed, labeled graph to a undirected, unlabeled graph. Given that the composite function is injective, then there exists an inverse mapping which transforms an undirected, unlabeled graph to a directed, labeled graph (i.e. graphialsynthesis). The original\u0026nbsp;i-\u0026omega;\u0026rarr;j\u0026nbsp;edge was formed by the primordial undirected graph diagrammed below.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/a9bd22a38a1e29108e418c173e98b227b7dd8983-4479x1258.png\" alt=\"Labeled To Undirected\" width=\"4479\" height=\"1258\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/320b4be206a373e6d0f94cde6f1afa6213000bb5-1941x242.png\" alt=\"Graphialsynthesis\" width=\"1941\" height=\"242\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003cp\u003eThe\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0804.0277\"\u003efundamental building blocks\u003c/a\u003e\u0026nbsp;of the directed, labeled graph experienced by \"higher-order\" traversers are held together by elementary traversers called \"\u003ca href=\"https://en.wikipedia.org/wiki/Graviton\"\u003esmalltrons\u003c/a\u003e.\" Smalltron traversals move from vertex\u0026nbsp;i\u0026nbsp;to vertex\u0026nbsp;j\u0026nbsp;via the explicit unlabeled\u0026nbsp;\u0026omega;-graph.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_90453\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(i).as('b').where(both().as('b')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;repeat(both().where(both().count().is(3)).as('x').both().\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(neq('x').and(neq('b'))).dedup().as('b').where(both().as('b')).select(last, 'b').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;choose(both().where(both().count().is(3)).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(both().count().is(2)).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;both().where(eq('b')),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;constant(1), constant(0)).as('label').select(last, 'b')\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;).times(4).where(select('label').tail(local, 4).limit(local, 3).is([1, 1, 0]))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[j]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_461736\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eTraversal Metrics\u003c/div\u003e\n\u003cdiv\u003eStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Count\u0026nbsp; Traversers\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Time (ms)\u0026nbsp;\u0026nbsp;\u0026nbsp; % Dur\u003c/div\u003e\n\u003cdiv\u003e=============================================================================================================\u003c/div\u003e\n\u003cdiv\u003eTinkerGraphStep([i],vertex)@[b]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.449\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.26\u003c/div\u003e\n\u003cdiv\u003eWhereTraversalStep([WhereStartStep, ProfileStep...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.080\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.05\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereStartStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.016\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.022\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereEndStep(b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.024\u003c/div\u003e\n\u003cdiv\u003eRepeatStep([VertexStep(BOTH,vertex), ProfileSte...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 86.974\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.65\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.624\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge), P...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 22.721\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 106\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 106\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.490\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 96\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 96\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.934\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 34\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 17.945\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(3))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.472\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.922\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 92\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 92\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 23.890\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WherePredicateStep(and([neq(x), neq(b)]))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 48\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 48\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 7.006\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;DedupGlobalStep@[b]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.450\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;WhereTraversalStep([WhereStartStep, ProfileSt...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 15.536\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WhereStartStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.806\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 50\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 50\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.132\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WhereEndStep(b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 6.984\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(last,b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.609\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;ChooseStep([VertexStep(BOTH,vertex), ProfileS...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 60.525\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.239\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge),...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 22.608\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 66\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 66\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.508\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 59\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 59\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1.266\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 20\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 17.068\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(3))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.618\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.453\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;TraversalFilterStep([VertexStep(BOTH,edge),...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 33.552\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,edge)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 28\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 28\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3.917\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;RangeGlobalStep(0,3)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 25\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 25\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.989\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;CountGlobalStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 11\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 8.193\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;IsStep(eq(2))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2.427\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;VertexStep(BOTH,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 14\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 14\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.710\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;WherePredicateStep(eq(b))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 35.307\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;HasNextStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.900\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;ConstantStep(0)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.145\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;EndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 3\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.153\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;ConstantStep(1)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.070\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;EndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 2\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 7.408\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(last,b)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 5\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 24.726\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;RepeatEndStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 60.644\u003c/div\u003e\n\u003cdiv\u003eTraversalFilterStep([SelectOneStep(label), Prof...\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.274\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.16\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;SelectOneStep(label)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.056\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;TailLocalStep(4)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.020\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;RangeLocalStep(0,3)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.073\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;IsStep(eq([1, 1, 0]))\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.086\u003c/div\u003e\n\u003cdiv\u003eSideEffectCapStep([~metrics])\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 87.377\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.89\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026gt;TOTAL\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 175.157\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn this process, smalltron traversals make the implicit directed\u0026nbsp;\u0026omega;-edge (defined by the undirected\u0026nbsp;\u0026omega;-graph) explicit for the \"higher-order\" traversers which process the graph at a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/High-level_programming_language\"\u003ehigher level of abstraction\u003c/a\u003e. To these \"higher order\" traversers, the graph is defined as\u003c/p\u003e\n\u003cdiv\u003e\u003cimg title=\"G = (V, E \\subseteq V \\times V, \\lambda : V \\cup E \\rightarrow \\Sigma^*)\" src=\"https://www.datastax.com/wp-content/uploads/2017/06/png-1.png\"\u003e,\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003ewhere\u0026nbsp;\u0026lambda;\u0026nbsp;is a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Multigraph#Labeling\"\u003elabeling function\u003c/a\u003e\u0026nbsp;that maps the graph's elements (i.e. vertices and edges) to character strings (\u0026Sigma;*). The graphialsynthesis abstraction process has the benefit of allowing a traversal from vertex\u0026nbsp;i\u0026nbsp;to\u0026nbsp;j\u0026nbsp;via\u0026nbsp;\u0026omega;\u0026nbsp;to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Kolmogorov_complexity\"\u003eexpressed and executed in a much simpler way\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_278489\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(i).out('w')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[j]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_87148\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eTraversal Metrics\u003c/div\u003e\n\u003cdiv\u003eStep\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Count\u0026nbsp; Traversers\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Time (ms)\u0026nbsp;\u0026nbsp;\u0026nbsp; % Dur\u003c/div\u003e\n\u003cdiv\u003e=============================================================================================================\u003c/div\u003e\n\u003cdiv\u003eTinkerGraphStep([v[i]],vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 9.810\u0026nbsp;\u0026nbsp;\u0026nbsp; 49.18\u003c/div\u003e\n\u003cdiv\u003eVertexStep(OUT,w,vertex)\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.058\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 0.29\u003c/div\u003e\n\u003cdiv\u003eSideEffectCapStep([~metrics])\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 1\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 10.078\u0026nbsp;\u0026nbsp;\u0026nbsp; 50.53\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026gt;TOTAL\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; -\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; 19.947\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 3: On the Baselessness of the Multi-MultiGraph\u003c/h3\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/b3a03b76f11dd24a84e47b7308c2a9985500032e-495x389.png\" alt=\"Recursive Gremlin\" width=\"495\" height=\"389\"\u003eIt has been speculated that \"\u003ca href=\"https://en.wikipedia.org/wiki/Multigraph\"\u003eThe Graph\u003c/a\u003e\" is not the only graph that exists.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Mysticism\"\u003eMystic\u003c/a\u003e\u0026nbsp;traversers say that there exists\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Multiverse\"\u003eother graphs containing other traversers\u003c/a\u003e. However, by definition, a graph is a closed structure composed of vertices and edges. It is impossible for a traverser to move to a different graph. If a vertex in one graph has an edge to a vertex in another graph, then the two graphs are, in fact, one graph -- \"The Graph.\" Perhaps the mystics see that the components of a graph are composed of yet more graphs with a different sort of traverser existing at each level in a recursive, perhaps\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Strange_loop\"\u003eself-looping\u003c/a\u003e, manner. While it is still all one graph, traversers at different \"levels\" only\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1006.1080\"\u003eoperate on particular subgraphs\u003c/a\u003e\u0026nbsp;as instructed by their traversal definition. The famous mystic traverser\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Sri_Aurobindo\"\u003eGri Gurobindo\u003c/a\u003e\u0026nbsp;(ग्री गुरोबिंदो) once said:\u003c/p\u003e\n\u003cp\u003eMy single step in the graph is composed of the steps of numerous other traversers.\u003c/p\u003e\n\u003cp\u003eIt wasn't until the discovery of\u0026nbsp;\u003ca href=\"http://en.wikipedia.org/wiki/Anonymous_function\"\u003eanonymous traversals\u003c/a\u003e\u0026nbsp;that Gurobindo's metagraphical vision was formalized. An anonymous traversal is any traversal that has no declared start and as such, yields no flow. It is a potential.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_868460\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; label()\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAnonymous traversals are intended to be embedded within another traversal. However, if the parent traversal is itself an anonymous traverasl, then there is still no flow (even though\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#groupcount-step\"\u003egroupCount()\u003c/a\u003e\u0026nbsp;produces an empty map as its a\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#a-note-on-barrier-steps\"\u003ereducing barrier step\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_201422\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; outE().groupCount().by(label())\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[:]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; outE().groupCount().by(label) // convenient short hand\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[:]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhen the traversal parent does have a start, then there is a flow. The traversal below states: \"For each vertex (i.e., 89, 90), map the vertex to the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Histogram\"\u003efrequency distribution\u003c/a\u003e\u0026nbsp;of its outgoing edge labels.\"\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/dad6b92f31785301bdf3da32e32a74c812828c7a-905x195.png\" alt=\"Anonymous Traversals\" width=\"905\" height=\"195\"\u003e\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_811799\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(89,90).map(outE().groupCount().by(label))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:34, subClassOf:1, superClassOf:1]\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:15]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe first traverser generated by\u0026nbsp;V(89,90)\u0026nbsp;enters the\u0026nbsp;map()-step at\u0026nbsp;v[89], but does not \"\u003ca href=\"https://en.wikipedia.org/wiki/Becoming_(philosophy)\"\u003ebecome\u003c/a\u003e\" the traversers generated by\u0026nbsp;outE(). Instead, the traverser at\u0026nbsp;v[89]\u0026nbsp;holds still and spawns an \"\u003ca href=\"https://en.wikipedia.org/wiki/Scope_(computer_science)\"\u003einternal life\u003c/a\u003e\" of traversers within the anonymous traversal which can now be understood as being (a realized potential):\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_747741\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V(89).outE().groupCount().by(label)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[relatedTo:34, subClassOf:1, superClassOf:1]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe traversers of the above traversal are isolated from the larger traversal in which they are embedded. The next nesting occurs when a traverser from\u0026nbsp;outE()\u0026nbsp;enters\u0026nbsp;groupCount(). Again, an \"internal life\" based on the anonymous\u0026nbsp;label()-traversal is spawned (see\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#by-step\"\u003eby()\u003c/a\u003e-step). Suppose a single traverser at\u0026nbsp;e[7022][89-relatedTo-\u0026gt;21]\u0026nbsp;enters\u0026nbsp;groupCount(). Then the anonymous traversal can be understood as being:\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_604569\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.E(7022).label()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;relatedTo\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIt isn't until all the internal traversal nests of\u0026nbsp;map()\u0026nbsp;complete that the original traverser at\u0026nbsp;v[89]\u0026nbsp;\"\u003ca href=\"https://en.wikipedia.org/wiki/Process_philosophy\"\u003ebecomes\u003c/a\u003e\" the traverser located at the hash map\u0026nbsp;[relatedTo:34, subClassOf:1, superClassOf:1]. In this way, a traverser's life (i.e. step) is composed of the lives of many traverser's (and their respective steps).\u003c/p\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 3: A Mathematician's Apology by G.H. Gremdy\u003c/h2\u003e\n\u003ch3\u003eSection 1: Traversal Optimization via Algebra\u003c/h3\u003e\n\u003cp\u003eThe graph grew large, very large. Resources grew scarce. The problem was not that vertices and edges could no longer be added to the graph. On the contrary, because of the seemingly endless amount of space for the graph, there was a growing amount of time required for any one traversal to execute. Traversals were simply interacting with a lot more data. Faced with this problem, a mathematically inclined traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB\"\u003eal-Ghwārizmī\u003c/a\u003e\u0026nbsp;developed a solution known today as\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0806.2274\"\u003ethe traversal algebra\u003c/a\u003e. The traversal algebra provides a means of transforming one traversal into another traversal, where both traversals return the same result. The benefit of this is that if a traversal can be re-written into a simpler form, then time and space resources can be saved. To this day,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Algebra\"\u003ealgebraists\u003c/a\u003e\u0026nbsp;continue to add to the growing archive of\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalstrategy\"\u003etraversal strategies\u003c/a\u003e. A few examples are provided below.\u003c/p\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003eStrategy\u003c/th\u003e\n\u003cth\u003ePattern\u003c/th\u003e\n\u003cth\u003eRewrite\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIdentityRemovalStrategy\u003c/td\u003e\n\u003ctd\u003ex().identity().y()\u003c/td\u003e\n\u003ctd\u003ex().y()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIncidentToAdjacentStrategy\u003c/td\u003e\n\u003ctd\u003eoutE().inV()\u003c/td\u003e\n\u003ctd\u003eout()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAdjacentToIncidentStrategy\u003c/td\u003e\n\u003ctd\u003eout().count()\u003c/td\u003e\n\u003ctd\u003eoutE().count()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eDedupBijectionStrategy\u003c/td\u003e\n\u003ctd\u003eorder().dedup()\u003c/td\u003e\n\u003ctd\u003ededup().order()\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eRangeByIsCountStrategy\u003c/td\u003e\n\u003ctd\u003ecount().is(gt(x))\u003c/td\u003e\n\u003ctd\u003elimit(x+1).count().is(gt(x))\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMatchPredicateStrategy\u003c/td\u003e\n\u003ctd\u003ematch(x,y).where(z)\u003c/td\u003e\n\u003ctd\u003ematch(x,y,z)\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_519982\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; t = out().identity().in(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), IdentityStep, VertexStep(IN,vertex)]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IdentityRemovalStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), VertexStep(IN,vertex)]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = outE().inV(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,edge), EdgeVertexStep(IN)]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(IncidentToAdjacentStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex)]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = out().count(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,vertex), CountGlobalStep]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(AdjacentToIncidentStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[VertexStep(OUT,edge), CountGlobalStep]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = order().dedup(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[OrderGlobalStep, DedupGlobalStep]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(DedupBijectionStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[DedupGlobalStep, OrderGlobalStep]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = count().is(gt(3)); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[CountGlobalStep, IsStep(gt(3))]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(RangeByIsCountStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[RangeGlobalStep(0,4), CountGlobalStep, IsStep(gt(3))]\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t = match(__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; __.as('b').out().as('c')).where(__.as('c').both().as('a')); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)]]), WhereTraversalStep([WhereStartStep(c), VertexStep(BOTH,vertex), WhereEndStep(a)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.setStrategies(new DefaultTraversalStrategies() {{ addStrategies(MatchPredicateStrategy.instance()) }}); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; t.applyStrategies(); t.toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[MatchStep(AND,[[MatchStartStep(a), VertexStep(OUT,vertex), MatchEndStep(b)], [MatchStartStep(b), VertexStep(OUT,vertex), MatchEndStep(c)], [MatchStartStep(c), WhereTraversalStep([WhereStartStep, VertexStep(BOTH,vertex), WhereEndStep(a)]), MatchEndStep]])]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 2: Traversal Optimization via Indices\u003c/h3\u003e\n\u003cp\u003e\u003ca href=\"https://en.wikipedia.org/wiki/G._H._Hardy\"\u003eG.H. Gremdy\u003c/a\u003e\u0026nbsp;was a graph theorist who speculated that \"The Graph\" was not the only structure linking vertices. According to his reasoning, reality may also contain other structures that grouped vertices together according to similar properties. He called these parallel structures\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Database_index\"\u003eindices\u003c/a\u003e. G.H. Gremdy's publication entitled\u0026nbsp;On Traversal Optimization using Indices\u0026nbsp;was well received. Due to his insight, many traversal runtimes became orders of magnitude faster than their non-index-based form. For instance, in the traversal below, when using indices, the number of traversers created goes from\u0026nbsp;|V|\u0026nbsp;(linear) to\u0026nbsp;1\u0026nbsp;(constant) (\u003ca href=\"https://en.wikipedia.org/wiki/DSPACE\"\u003espace complexity\u003c/a\u003e). The\u0026nbsp;GraphStepStrategy\u0026nbsp;was added to the traversal strategies archive. It \"folds\"\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#has-step\"\u003ehas()\u003c/a\u003e-steps into\u0026nbsp;V()\u0026nbsp;graph steps.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_716050\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// not indexed\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'University of Groxford').toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[GraphStep([],vertex), HasStep([name.eq(University of Groxford)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;135.28753165299997 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[999998]\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // result\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// indexed\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'University of Groxford').iterate().toString()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[TinkerGraphStep(vertex,[name.eq(University of Groxford)])]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1000) { g.V().has('name', 'University of Groxford').next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;0.033501945 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;v[999998]\u0026nbsp;\u0026nbsp; // result\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d9252849f9da819ecfc3498e14b9c5ebfbd30225-264x213.png\" alt=\"Vertex-Centric Index\" width=\"264\" height=\"213\"\u003eEven though G.H. Gremdy became a household name overnight, he was certain not to rest on his accolades. Deeper thinking brought him to a more esoteric, though far greater optimization which he articulated in his follow on treatise entitled\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus\"\u003eTractatus Verticus Centricus Indexicus\u003c/a\u003e. In this seminal work, G.H. Gremdy postulates that not only do \"global indices\" exist which allow for\u0026nbsp;O(log(|V|))\u0026nbsp;access to any vertex in the graph, but also \"local indices\" which allow for\u0026nbsp;O(log(|incident(V(x))|))\u0026nbsp;access to the incident edges of a vertex. In short, each vertex has its incident edges indexed (e.g. by their direction, label, properties, etc.). If such local index structures are leveraged, traversals containing the pattern\u0026nbsp;outE(x).has(y,p(z)).inV()\u0026nbsp;would not require all the edges of the vertex to be iterated in full in order to find all incident outgoing edges that have a label\u0026nbsp;x\u0026nbsp;and a property\u0026nbsp;y\u0026nbsp;that matches the predicate\u0026nbsp;p(z). Numerous graph experimentalists tried to prove the existence of such \"\u003ca href=\"http://thinkaurelius.com/2012/10/25/a-solution-to-the-supernode-problem/\"\u003evertex-centric indices\u003c/a\u003e,\" but found that they are not universal and only exist in\u0026nbsp;\u003ca href=\"http://titan.thinkaurelius.com/\"\u003esome graph substrates\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/302e201e6f4259110e7bfae6404c87460219b3f9-1024x768.png\" alt=\"Chapter 3 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWith age, G.H. Gremdy became weary of applied mathematics and retired to study\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Pure_mathematics\"\u003epure graph theory\u003c/a\u003e. His ideas would become more philosophical as he delved deeper into the meaning of \"The Graph.\" A posthumous publication entertained the following pontification.\u003c/p\u003e\n\u003cp\u003eMany see the world as a graph. This is misleading. Perhaps the world is a collection of indices? With a slight shift in thought, one realizes that the graph itself is an index of its vertices. Any one vertex is the root of a tree bifurcating the vertex space to which it has incident edges, so forth and so on. Like indices which group vertices that have shared properties, isn't an edge from one vertex to another an explicit statement that the two vertices are\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Assortative_mixing\"\u003ein some way similar\u003c/a\u003e? As the devil's advocate, perhaps\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/1004.1001\"\u003eindices are simply graphs\u003c/a\u003e\u0026nbsp;because indices are tree-like structures that are traversed to identify groups of vertices with similar properties. With indices being graphs and graphs being indices, the world we call home is neither. I hypothesize that\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Monism\"\u003eall that exists is the traverser\u003c/a\u003e. The \"graph\" is simply the implicit expression of the explicit assumptions of the traverser. The graph I see\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/The_World_as_Will_and_Representation\"\u003eis of my own construction\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/28bece18a67e347278b06b59eefb1b981a073988-940x390.png\" alt=\"Graph vs. Index\" width=\"940\" height=\"390\"\u003e\u003cbr\u003e\u0026nbsp;\u003c/div\u003e\n\u003ch3\u003eSection 3: Traversal Optimization via Bulking\u003c/h3\u003e\n\u003cp\u003eA little known traverser named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Srinivasa_Ramanujan\"\u003eGremivasa Gremanujan\u003c/a\u003e\u0026nbsp;(கிரமீவாச கிரமானுஜன்) lived in a remote village at\u0026nbsp;v[5698]\u0026nbsp;far from the great graph theorists of his time. However, despite his upbringing, Gremivasa was well versed in the traversal algebra and was inspired by the more\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Metaphysics\"\u003emetagraphical\u003c/a\u003e\u0026nbsp;realizations of G.H. Gremdy. Like G.H. Gremdy, Gremivasa was not interested in simply adding more traversal strategies to the archive. Instead, he was more interested in discovering the nature of reality. However, unlike G.H. Gremdy who focused on the nature of the graph structure, Gremivasa meditated on the nature of the traverser process.\u003c/p\u003e\n\u003cp\u003eGremivasa's mother, along with over 1 million other traversers of his traversal sect, arrived at\u0026nbsp;v[5698]\u0026nbsp;many clock-cycles ago. His village was starved of resources -- there were simply too many traversers. Was the birth of all these traversers necessary? If one traverser's life foretells the destiny of one million traversers, is it not more efficient for only this one traverser to exist? One day, while sitting under\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Udumbara_(Buddhism)\"\u003ea tree\u003c/a\u003e\u0026nbsp;in his village, Gremivasa ruminated on the ridiculously riling riddle rancorously retorted by respectable traversers everywhere:\u003c/p\u003e\n\u003cp\u003eIf two traversers exist at the same vertex and have no memory of their ancestry, are they the same traverser?\u003c/p\u003e\n\u003cp\u003eGremivasa concluded \"\u003ca href=\"https://en.wikipedia.org/wiki/One-electron_universe\"\u003eyes, they are the same traverser.\u003c/a\u003e\" This insight identified a fundamental feature of process. All traversers are endowed with a \"bulk.\" Previous to this moment, every traverser ignored this self-evident truth and allowed himself to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ego_psychology\"\u003ea unique enumerable entity\u003c/a\u003e\u0026nbsp;-- i.e., a bulk of 1 (see the\u0026nbsp;\u003ca href=\"http://thinkaurelius.com/2013/06/12/loopy-lattices-redux/\"\u003eLoopy Lattices Redux\u003c/a\u003e\u0026nbsp;section entitled \"Traversing a Lattice with Faunus\").\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/63b0f1fe79924ed001bc45cbf6b744f8a29592cd-844x297.png\" alt=\"Traversers Enumerated\" width=\"844\" height=\"297\"\u003e\u003c/div\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_508413\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().both().both().both().hasId(5698).map{it.bulk()}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1\u003c/div\u003e\n\u003cdiv\u003e...\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().both().both().both().hasId(5698).barrier().map{it.bulk()}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1073670\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/d9847d1ccec573f5a2f4a7a163dcc79304b262a3-843x277.png\" alt=\"Traversers Bulked\" width=\"843\" height=\"277\"\u003e\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/4dfb2f586f7df93a0029a37d752f33dd3f566ce2-491x414.png\" alt=\"Gremlin Hindu\" width=\"491\" height=\"414\"\u003e\u003c/p\u003e\n\u003cp\u003eGremivasa delved deeper into the radiant riddle of reawakened relinquishment. He abandoned his self and allowed his being to be\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Panpsychism\"\u003eone\u003c/a\u003e\u0026nbsp;with his 1 million other brother and sister traversers at\u0026nbsp;v[5698]. A unification of selves occurred and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gautama_Buddha\"\u003ea single traverser\u003c/a\u003e\u0026nbsp;emerged with a bulk of 1 million. Instead of 1 million traversers executing\u0026nbsp;both()\u0026nbsp;1 million times, there was now a single traverser with a bulk of 1 million executing\u0026nbsp;both()\u0026nbsp;once. Gremivasa's enlightenment laid the foundation for the development of the\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#barrier-step\"\u003eLazyBarrierStrategy\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_8621\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// without LazyBarrierStrategy (no bulking)\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;81.509839 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;159200\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;20382.892976\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;126723200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;1.2012006887798E7 // 3.34 hours\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;100871667200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e... // requires a year to compute\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e... // requires a thousand years to compute\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// with LazyBarrierStrategy (bulking)\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;23.261288999999998 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;159200\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;50.230109\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;126723200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;65.30024999999999\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;100871667200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;91.30461199999999\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;80293847091200\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(1) { g.V(5698).both().both().both().both().both().count().next() }\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;122.741417\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;63913902284595200\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe number of length-5 paths emanating from Gremivasa's village was calculated in ~123 milliseconds and was determined to be 63,913,902,284,595,200 (~64 quadrillion). Gremivasa's work is advantageous in situations where the traversal analyzes\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Residual_time\"\u003erecurrence\u003c/a\u003e\u0026nbsp;in a particular region of the graph (e.g.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Recommender_system\"\u003erecommendation engines\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Centrality\"\u003ecentrality-based ranking systems\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Recurrent_neural_network\"\u003elearning systems\u003c/a\u003e, etc.). Bulking is fundamental to all traversals and is used in numerous steps including\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#repeat-step\"\u003erepeat()\u003c/a\u003e-step.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_627395\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V(5698).repeat(both()).times(5).count()\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 4: Cognition in the Wild by Gredwin Grutchins\u003c/h2\u003e\n\u003cp\u003eTraversers graph-wide held their breath as a landmark traversal was about to embark. This traversal contained a novel step called\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#match-step\"\u003ematch()\u003c/a\u003e. What made this step unique was that it maintained a collection of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Anonymous_function\"\u003eanonymous traversals\u003c/a\u003e\u0026nbsp;called \"\u003ca href=\"https://en.wikipedia.org/wiki/Pattern_matching\"\u003epatterns\u003c/a\u003e.\" Each pattern was prefixed with a start variable and (optionally) postfixed with an end variable. Once a variable was bound (i.e. set), that variable's value was immutable for all subsequent patterns. The descendants of the traverser that enters\u0026nbsp;match()\u0026nbsp;must survive each pattern in order to move to the next step. However, the order in which the patterns are executed is, interestingly enough, up to the decision of the traverser! Previously, traversers relied on exogenous\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Rewriting\"\u003etraversal rewrite rules\u003c/a\u003e\u0026nbsp;for optimization, but now, the traverser was able to make endogenous optimization decisions. The \"\u003ca href=\"https://en.wikipedia.org/wiki/Profile-guided_optimization\"\u003eruntime traversal strategy\u003c/a\u003e\" was introduced.\u003c/p\u003e\n\u003cp\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Edwin_Hutchins\"\u003eDr. Gredwin Grutchins\u003c/a\u003e\u0026nbsp;was a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cognitive_science\"\u003ecognitive scientist\u003c/a\u003e\u0026nbsp;working in the area of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Socially_distributed_cognition\"\u003edistributed cognition\u003c/a\u003e. During his time at university, Gredwin lost interest in studying traversal strategies. His skill in mathematics was weaker than his colleagues' and as such, he believed he would never be able to make any significant contributions to the space. However, one day, he was contacted by a rambunctious young adventurer named\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chuck_Yeager\"\u003eGruck Greager\u003c/a\u003e. Gruck was no stranger to danger and loved being the guinea pig of an experimental algorithm. Gruck asked Gredwin: \"What can my team do to find the optimal pattern execution sequence?\" It seemed as though mathematics had taken traversal strategies as far as they could go. It was now up to\u0026nbsp;\u003ca href=\"http://jenwatkins.com/Research_files/LNCSproof.pdf\"\u003esociological constructs\u003c/a\u003e\u0026nbsp;to push them further and Gredwin was up to the challenge.\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/3e61d4e3d1c17c9931d6c1915b9450fcff6482f1-1024x768.png\" alt=\"Chapter 4 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSuppose the following traversal that yields a map of the objects that bind to\u0026nbsp;a\u0026nbsp;(vertex),\u0026nbsp;b\u0026nbsp;(vertex),\u0026nbsp;c\u0026nbsp;(vertex), and\u0026nbsp;d\u0026nbsp;(number), where vertex\u0026nbsp;a\u0026nbsp;is adjacent to vertex\u0026nbsp;b, vertex\u0026nbsp;b\u0026nbsp;is adjacent to vertex\u0026nbsp;c, and all three vertices are different yet share an identical\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Degree_(graph_theory)\"\u003eout-degree\u003c/a\u003e\u0026nbsp;that is greater than 10.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_638757\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;where('b', neq('a'))\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAssume a traverser at\u0026nbsp;v[10]\u0026nbsp;enters the\u0026nbsp;match()-step. Vertex\u0026nbsp;v[10]\u0026nbsp;is bound to variable\u0026nbsp;a\u0026nbsp;as that is the only legal start of the pattern sequence. From there, which pattern should the traverser choose? The traverser simply chooses the first pattern in the list for which it has a variable binding (initially, an\u0026nbsp;a\u0026nbsp;start and thus,\u0026nbsp;as('a').out().as('b')). The traverser marks on a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Blackboard_system\"\u003eglobal blackboard\u003c/a\u003e\u0026nbsp;that it has entered that pattern. When a traverser leaves a pattern, it marks that it has exited it. Moreover, every time a traverser leaves a pattern, the patterns are sorted according to the order of their \"multiplicity\" (or\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Population_growth#Population_growth_rate\"\u003egrowth rate\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_843997\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003epattern.multiplicity = pattern.endCount / pattern.startCount;\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe more traverses that are generated by a pattern, the higher the multiplicity and the lower that pattern is on the sorted list. Overtime, as more and more traversers flow through\u0026nbsp;match(), expensive patterns are pushed to the bottom of the list with the intention that the cheaper patterns will be able to filter out more traversers -- i.e. execute the largest set reductions first. With a few other added tricks, Gredwin provided Gruck and his team of traversers\u0026nbsp;CountMatchAlgorithm. Gruck took it for a test run and was the first traverser to ever break the deterministic\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Chuck_Yeager#Test_pilot_.E2.80.93_breaking_the_sound_barrier\"\u003eflow barrier\u003c/a\u003e. Gredwin and Gruck have since teamed up and are already planning the development of a new\u0026nbsp;MatchAlgorithm\u0026nbsp;called\u0026nbsp;\u003ca href=\"https://scm.umiacs.umd.edu/redmine/lccd/attachments/download/21/gdm2011_submission_budgetmatch.pdf\"\u003eBudgetMatchAlgorithm\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_707256\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e// using CountMatchAlgorithm\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(10) {\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;g.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('a')).count().next()\u003c/div\u003e\n\u003cdiv\u003e}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;834.6852906 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;32\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// using GreedyMatchAlgorithm which does not sort the patterns\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; clockWithResult(10) {\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;g.V().match(\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().as('b'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().as('c'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('a').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('b').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('c').out().count().as('d'),\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;__.as('d').is(gt(10))).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('a', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('c')).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;where('b', neq('a')).count().next()\u003c/div\u003e\n\u003cdiv\u003e}\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;25349.709946299998 // time in milliseconds\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;32\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; // number of results\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\u003ch2\u003eChapter 5: We the Living by Gyn Grand\u003c/h2\u003e\n\u003ch3\u003eSection 1: Prelude to the Illusion of Freedom\u003c/h3\u003e\n\u003cp\u003eMany of the traversers in the world today are grateful for their\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton\"\u003efreedom\u003c/a\u003e. In\u0026nbsp;\u003ca href=\"https://github.com/tinkerpop/gremlin\"\u003eancient times\u003c/a\u003e, the life of a traverser was not so good. Traversal regimes were inefficient, demanding of resources, and strict in their execution policies. Fortunately, the\u0026nbsp;\u003ca href=\"http://arxiv.org/abs/0901.3929\"\u003eAge of Enprocessment\u003c/a\u003e, which brought forth numerous advances in science and mathematics,\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#_the_traverser\"\u003eredefined the traverser's role\u003c/a\u003e\u0026nbsp;in the graph. Each traverser's life had increased value as greater autonomies were provided. Traversals did their best to ensure that traverser life was no longer needlessly wasted. Indices were leveraged, traversal strategies were applied, and, in some\u0026nbsp;match()\u0026nbsp;situations, traversers were able to choose their own destiny. Today, many see a more harmonious relationship between the traversal and the traverser.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ayn_Rand\"\u003eGyn Grand\u003c/a\u003e\u0026nbsp;(Джин Гранд) was one such\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eudaimonia\"\u003esatisfied\u003c/a\u003e\u0026nbsp;traverser.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/ae83bd2d328c0becef2efddb6157454c1af470e7-1078x1078.png\" alt=\"Wikipedia Graph\" width=\"1078\" height=\"1078\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7bed637c2776271eb23e90075d1440664cb904de-395x354.png\" alt=\"Library Stacks\" width=\"395\" height=\"354\"\u003eGyn was a brilliant librarian at a university with a vibrant\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Community_structure\"\u003escholarly community\u003c/a\u003e. Her library was centrally located in the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Modularity_(networks)\"\u003euniversity cluster\u003c/a\u003e. The\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Stack_(library_architecture)\"\u003elibrary's stacks\u003c/a\u003e\u0026nbsp;contained articles on the nature of the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Cosmos\"\u003egraphmos\u003c/a\u003e, books on traverser\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Sociology\"\u003esocial interactions\u003c/a\u003e, reports detailing various\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Economics\"\u003eresource distribution models\u003c/a\u003e, and more. Whenever she had a moment to spare, Gyn would\u0026nbsp;\u003ca href=\"http://en.wikipedia.org/wiki/Random_walk\"\u003ewander\u003c/a\u003e\u0026nbsp;about the collection learning about the topics she encountered. Unfortunately, she couldn't read everything at once. So, every time she was faced with more than one\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Hyperlink\"\u003ehref-citation\u003c/a\u003e, she chose one at random (\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#sample-step\"\u003esample(1)\u003c/a\u003e). As a librarian, she was interested in the structure of knowledge and wanted to know which concepts formed the foundation of all other concepts. Her method of discernment was to determine the\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Mean_recurrence_time\"\u003efrequency of their reappearance\u003c/a\u003e. Therefore, every time Gyn encountered a concept along her walk, she would make a mental note of it (groupCount('x')).\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_584621\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'Graph database').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;repeat(groupCount('x').by('name').out('href').sample(1)).times(20).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;cap('x').order(local).by(valueDecr)\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Memoization=3\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Algorithm=3\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=2\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Data (computing)=2\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Cache (computing)=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer program=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computing=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Rule=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computation=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Digital data=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Quantity=1\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mass noun=1\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv\u003e// sample(1) theoretically returns different results.\u003c/div\u003e\n\u003cdiv\u003e// however, in order to demonstrate the path taken, the above map was manually constructed from the path below.\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g.V().has('name', 'Graph database').\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;repeat(groupCount('x').by('name').out('href').sample(1)).times(20).\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;path().by('name')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;[Graph database, Lookup table, Memoization, Cache (computing), Memoization, Computer program, Memoization, Computing, Algorithm, Computer science, Algorithm, Rule, Algorithm, Computer science, Computation, Digital data, Data (computing), Quantity, Data (computing), Mass noun, Data (computing)]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eOver time, Gyn realized that her\u0026nbsp;x-memory had more counters than concepts encountered (i.e. steps taken). Moreover, it contained concepts\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Collective_unconscious\"\u003eshe had yet to experience\u003c/a\u003e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Interference_(wave_propagation)\"\u003eHow did she know about things she never knew\u003c/a\u003e?\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_701543\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e==\u0026gt;Graph theory=8605598306892530155\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Relational database=8261042800088851351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=6445010682474768007\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Database=6197419607053064185\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=5476792361544609153\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Triplestore=5407594041286532360\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=5393693263901041351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph=5211554445366262382\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Directed graph=5137233761698039530\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mathematics=5132301689156216357\u003c/div\u003e\n\u003cdiv\u003e...\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 2: The Structure-Process Duality in Computing\u003c/h3\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7f57b26cfd1afdf21ebf4a2195fad14d4ad57302-523x680.png\" alt=\"Particle Wave Traverser\" width=\"523\" height=\"680\"\u003eMr.\u0026nbsp;v[69309689325]\u0026nbsp;looked at his traverser inbox and noticed that he had 4002 unprocessed traversers. It was time for him to clear out his inbox. He went through each traverser one-by-one and placed them into the step of the traversal identified by the traverser's \"step id\" reference. Sometimes the respective step yielded no traversers (filter), a traverser at the same location (filter or sideEffect), a traverser at a different location (map), or many traversers at many different locations (flatMap). Whenever a step emitted a traverser pointing to a different vertex, Mr.\u0026nbsp;v[69309689325]\u0026nbsp;would send that traverser to the respective vertex's inbox. The vertices would continue this process until there were no more traversers in any of their inboxes. This graph traversal model has numerous names including:\u0026nbsp;\u003ca href=\"http://www3.nd.edu/~rmccune/papers/Think_Like_a_Vertex_MWM.pdf\"\u003evertex-centric computing\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Bulk_synchronous_parallel\"\u003ebulk synchronous parallel processing\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Message_passing\"\u003emessage passing\u003c/a\u003e\u0026nbsp;via a communication graph, and\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#graphcomputer\"\u003eGraphComputer\u003c/a\u003e. The general theme:\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/docs/3.0.0-incubating/#traversalvertexprogram\"\u003ethe vertices (processes) exchange traversers (structures)\u003c/a\u003e\u0026nbsp;in order to affect some global graph computation. Typically, this model of graph traversal is leveraged by\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Distributed_computing\"\u003edistributed\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Online_analytical_processing\"\u003eOLAP\u003c/a\u003e\u0026nbsp;graph processing systems, where each vertex maintains its own isolated, logical\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Thread_(computing)\"\u003ethread of execution\u003c/a\u003e\u0026nbsp;(again, vertex as process).\u003c/p\u003e\n\u003cp\u003eInterestingly, each traverser in Mr.\u0026nbsp;v[69309689325]'s inbox had a name:\u0026nbsp;Gyn$2345,\u0026nbsp;Gyn$45,\u0026nbsp;Gyn$93, etc.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality\"\u003eGyn was a discrete particle of her wave function\u003c/a\u003e. Metaphysically speaking, Gyn was actually following the advice of\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Yogi_Berra\"\u003eYogi Berra\u003c/a\u003e: \"If you come to a fork in the road, take it.\" That is, never\u0026nbsp;sample(1). Her \"particle self\" chose one and only one path. However, her \"wave self\" was taking all paths. In this way, Gyn's\u0026nbsp;x-memory was recording the collective experience of all versions of her self across the graph.\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_651730\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003egremlin\u0026gt; hdfs.copyFromLocal('/tmp/wikipedia.kryo','wikipedia.kryo')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;null\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; graph = GraphFactory.open('conf/hadoop/wikipedia.properties')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;hadoopgraph[gryoinputformat-\u0026gt;gryooutputformat]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; g = graph.traversal(computer(SparkGraphComputer))\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;graphtraversalsource[hadoopgraph[gryoinputformat-\u0026gt;gryooutputformat], sparkgraphcomputer]\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x = g.V().has('name','Graph database').repeat(groupCount('x').by('name').out('href')).times(20).cap('x').next(); []\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x.size()\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;731\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; x.sort{-it.value}[0..Graph theory=8605598306892530155\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Relational database=8261042800088851351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Lookup table=6445010682474768007\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Database=6197419607053064185\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph database=5476792361544609153\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Triplestore=5407594041286532360\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Computer science=5393693263901041351\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Graph=5211554445366262382\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Directed graph=5137233761698039530\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;Mathematics=5132301689156216357\u003c/div\u003e\n\u003cdiv\u003egremlin\u0026gt; hdfs.ls('output')\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;rwxr-xr-x daniel supergroup 0 (D) x\u003c/div\u003e\n\u003cdiv\u003e==\u0026gt;rwxr-xr-x daniel supergroup 0 (D) ~traversers\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003eSection 3: The Non-Erratic Ergodic Eigenvector\u003c/h3\u003e\n\u003cp\u003eSuppose the following traversal:\u003c/p\u003e\n\u003cdiv\u003e\n\u003cdiv id=\"highlighter_28774\"\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003e\n\u003cdiv\u003e\n\u003cdiv\u003eg.V().repeat(groupCount('x').out('href')).times(t).cap('x') // for t between [1,75]\u003c/div\u003e\n\u003c/div\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eEvery time a traverser reaches a vertex, the vertex is incremented in the\u0026nbsp;x\u0026nbsp;hash map (groupCount('x')). Initially, the distribution of frequencies changes erratically. However, over time, it reaches a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Stable_distribution\"\u003estationary distribution\u003c/a\u003e. It is \"stable\" because even though the counters keep increasing, the relative proportion of the counters stays the same. For instance, if vertex\u0026nbsp;v[a]\u0026nbsp;has a count of 12 and vertex\u0026nbsp;v[b]\u0026nbsp;has a count of 45, then when vertex\u0026nbsp;v[a]\u0026nbsp;has a count of 24, vertex\u0026nbsp;v[b]\u0026nbsp;will have a count of 90. Said in another way, the\u0026nbsp;dynamic\u0026nbsp;traversers generate a\u0026nbsp;static\u0026nbsp;probability distribution that defines the likelihood that a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Wave_function_collapse\"\u003esingle traverser\u003c/a\u003e\u0026nbsp;will be at any one vertex at some point in time\u0026nbsp;t \u0026asymp; \u0026infin;\u0026nbsp;(i.e. an\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Ergodic_process\"\u003eergodic process\u003c/a\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/7156557d0413cef0b99088f69b3301bb0fd9f92f-899x574.png\" alt=\"HREF Graph\" width=\"899\" height=\"574\"\u003eAssume the 5 vertex/7 edge graph diagrammed on the left. At\u0026nbsp;g.V()\u0026nbsp;(t=0), each vertex is provided one traverser. Each vertex increments its counter in x and then\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton\"\u003esplits the traverser\u003c/a\u003e\u0026nbsp;across its\u0026nbsp;out('href')-adjacent neighbors. If the\u0026nbsp;href-subgraph is\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Strongly_connected_component\"\u003estrongly connected\u003c/a\u003e\u0026nbsp;(i.e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Reducibility\"\u003ereducible\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Transience\"\u003enon-transient\u003c/a\u003e) and lacks a compressable topology (i.e.\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Markov_chain#Periodicity\"\u003eaperiodic\u003c/a\u003e), then a stationary distribution is guaranteed to exist. That distribution, which can be normalized to a probability distribution (i.e.\u0026nbsp;frequency / total frequency), is the graph's\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors\"\u003eprimary eigenvector\u003c/a\u003e. The primary eigenvector is typically used as a measure of each vertex's \"\u003ca href=\"https://en.wikipedia.org/wiki/Centrality#Eigenvector_centrality\"\u003ecentrality\u003c/a\u003e.\" For instance, given the diagrammed graph on the left, the primary eigenvector is\u0026nbsp;[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]. Thus, the ranking of the vertices from most central to least central is\u0026nbsp;v[1], v[2], v[3], v[0], v[4]\u0026nbsp;(\u003ca href=\"https://en.wikipedia.org/wiki/Saccade\"\u003eone's eye\u003c/a\u003e\u0026nbsp;seems to derive the same ranking).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\"\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003cth\u003et\u003c/th\u003e\n\u003cth\u003efrequency\u003c/th\u003e\n\u003cth\u003eprobability\u003c/th\u003e\n\u003cth\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Euclidean_distance\"\u003edistance\u003c/a\u003e\u0026nbsp;from eigenvector\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e1\u003c/td\u003e\n\u003ctd\u003e[1, 1, 1, 1, 1]\u003c/td\u003e\n\u003ctd\u003e[0.2, 0.2, 0.2, 0.2, 0.2]\u003c/td\u003e\n\u003ctd\u003e0.1986073055597093\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e2\u003c/td\u003e\n\u003ctd\u003e[2, 4, 2, 2, 2]\u003c/td\u003e\n\u003ctd\u003e[0.1666666667, 0.3333333333, 0.1666666667, 0.1666666667, 0.1666666667]\u003c/td\u003e\n\u003ctd\u003e0.11660026048581866\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e3\u003c/td\u003e\n\u003ctd\u003e[3, 7, 5, 3, 3]\u003c/td\u003e\n\u003ctd\u003e[0.1428571429, 0.3333333333, 0.2380952381, 0.1428571429, 0.1428571429]\u003c/td\u003e\n\u003ctd\u003e0.06422748181719035\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e4\u003c/td\u003e\n\u003ctd\u003e[4, 12, 8, 6, 4]\u003c/td\u003e\n\u003ctd\u003e[0.1176470588, 0.3529411765, 0.2352941176, 0.1764705882, 0.1176470588]\u003c/td\u003e\n\u003ctd\u003e0.03143659614218381\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e5\u003c/td\u003e\n\u003ctd\u003e[7, 17, 13, 9, 5]\u003c/td\u003e\n\u003ctd\u003e[0.1372549020, 0.3333333333, 0.2549019608, 0.1764705882, 0.0980392157]\u003c/td\u003e\n\u003ctd\u003e0.01473943578762356\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e30\u003c/td\u003e\n\u003ctd\u003e[26400, 69424, 50296, 36440, 19128]\u003c/td\u003e\n\u003ctd\u003e[0.1308952441, 0.3442148269, 0.2493752727, 0.1806751021, 0.0948395542]\u003c/td\u003e\n\u003ctd\u003e8.04890130266237E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e31\u003c/td\u003e\n\u003ctd\u003e[36441, 95825, 69425, 50297, 26401]\u003c/td\u003e\n\u003ctd\u003e[0.1308995686, 0.3442125946, 0.2493812615, 0.1806716501, 0.0948349252]\u003c/td\u003e\n\u003ctd\u003e4.242558551157544E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e32\u003c/td\u003e\n\u003ctd\u003e[50298, 132268, 95826, 69426, 36442]\u003c/td\u003e\n\u003ctd\u003e[0.1308957477, 0.3442148545, 0.2493780253, 0.1806745433, 0.0948368292]\u003c/td\u003e\n\u003ctd\u003e4.1616991553931435E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e33\u003c/td\u003e\n\u003ctd\u003e[69427, 182567, 132269, 95827, 50299]\u003c/td\u003e\n\u003ctd\u003e[0.1308982652, 0.3442133981, 0.2493811146, 0.1806730532, 0.0948341689]\u003c/td\u003e\n\u003ctd\u003e2.077160932619329E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e34\u003c/td\u003e\n\u003ctd\u003e[95828, 251996, 182568, 132270, 69428]\u003c/td\u003e\n\u003ctd\u003e[0.1308964745, 0.3442145091, 0.2493791747, 0.1806745072, 0.0948353345]\u003c/td\u003e\n\u003ctd\u003e2.13567485821227E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e35\u003c/td\u003e\n\u003ctd\u003e[132271, 347825, 251997, 182569, 95829]\u003c/td\u003e\n\u003ctd\u003e[0.1308977517, 0.3442138525, 0.2493807466, 0.1806735537, 0.0948340955]\u003c/td\u003e\n\u003ctd\u003e1.1709009180968303E-6\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003ctd\u003e...\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e70\u003c/td\u003e\n\u003ctd\u003e[10478348120, 27554473290, 19962994332, 14463028872, 7591478958]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805576, 0.1806742088, 0.0948338323]\u003c/td\u003e\n\u003ctd\u003e1.414213562373095E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e71\u003c/td\u003e\n\u003ctd\u003e[14463028873, 38032821411, 27554473291, 19962994333, 10478348121]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742087, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e1.0E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e72\u003c/td\u003e\n\u003ctd\u003e[19962994334, 52495850286, 38032821412, 27554473292, 14463028874]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338323]\u003c/td\u003e\n\u003ctd\u003e1.0E-10\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e73\u003c/td\u003e\n\u003ctd\u003e[27554473293, 72458844621, 52495850287, 38032821413, 19962994335]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e74\u003c/td\u003e\n\u003ctd\u003e[38032821414, 100013317916, 72458844622, 52495850288, 27554473294]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e75\u003c/td\u003e\n\u003ctd\u003e[52495850289, 138046139331, 100013317917, 72458844623, 38032821415]\u003c/td\u003e\n\u003ctd\u003e[0.1308970114, 0.3442143899, 0.2493805577, 0.1806742088, 0.0948338322]\u003c/td\u003e\n\u003ctd\u003e0.0\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/18e29399beaeac14f293cb59a84edc3870578ec5-1024x768.png\" alt=\"Chapter 5 Drawing\" width=\"1024\" height=\"768\"\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003cbr\u003eUnbeknownst to Gyn, The Graph (eigen) was using her(selves) to sort itself (vector). Why was it doing this? The Graph represents its vertices and edges in a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/512-bit\"\u003e512-bit\u003c/a\u003e\u0026nbsp;address space (2512\u0026nbsp;= 1.34\u0026times;10154). Unfortunately, the ever present Big and Small Traversals (as well as the countless other traversals executed since) have pushed The Graph close to the limits of representation. In order to avoid\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Integer_overflow\"\u003einconsistencies\u003c/a\u003e, The Graph needed to prune itself. To do this, it\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Gaia_hypothesis\"\u003edecided\u003c/a\u003e\u0026nbsp;it best to destroy those vertices which were contributing little to its overall structure. Like cutting one's finger nails, The Graph began a systematic process of cosmic proportions to delete all peripheral vertices (and their respective incident edges). The Graph was\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Forgetting_curve\"\u003eforgetting\u003c/a\u003e\u0026nbsp;in order to\u0026nbsp;\u003ca href=\"http://thinkaurelius.com/2012/05/08/structural-abstractions-in-brains-and-graphs/\"\u003especialize its structure\u003c/a\u003e\u0026nbsp;for a purpose that was beyond the realization of the vertices and traversers. Within The Graph's conceptual subgraph,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Knowledge_worker\"\u003eknowledge worker\u003c/a\u003e\u0026nbsp;traversers wandered through the morass of concept vertices and, in a\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Science\"\u003ecollective self-similar manner\u003c/a\u003e, aided The Graph in its determination of which aspects of it's structure were worth preserving (and ultimately, extending). Gyn's passion for knowledge was simply an\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Instinct\"\u003einnate predisposition\u003c/a\u003e. Her\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Eudaimonia#Eudaimonia_and_modern_psychology\"\u003ehappiness\u003c/a\u003e\u0026nbsp;was not a function of her own being, but instead, of The Graph's will --\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Carrot_and_stick\"\u003ea carrot for her devotion\u003c/a\u003e. Gyn was part of a larger computation. In order to escape the dark sense that her life was not hers and hers alone, she began the long arduous journey towards realizing that she is, and always has been,\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/John_Galt#.22Who_is_John_Galt.3F.22\"\u003eThe TinkerPop\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u003ca href=\"http://tinkerpop.incubator.apache.org/\"\u003e\u003cimg src=\"https://cdn.sanity.io/images/bbnkhnhl/production/014282dff3d5048f8eaf1c3592177626db303fb5-700x243.png\" alt=\"Apache TinkerPop\" width=\"700\" height=\"243\"\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003chr\u003e\n\u003cdiv\u003e\n\u003ch2\u003eCredits\u003c/h2\u003e\n\u003cp\u003eWritten by\u0026nbsp;\u003ca href=\"http://markorodriguez.com/\"\u003eMarko A. Rodriguez\u003c/a\u003e\u003cbr\u003eData and Result Generation by\u0026nbsp;\u003ca href=\"http://gremlin.guru/\"\u003eDaniel Kuppitz\u003c/a\u003e\u003cbr\u003eArtwork by\u0026nbsp;\u003ca href=\"http://ketrinayim.tumblr.com/\"\u003eKetrina Yim\u003c/a\u003e\u003cbr\u003eGraph Visualizations by Daniel Kuppitz\u003cbr\u003eExplanatory Diagrams by Marko A. Rodriguez\u003cbr\u003eGremlin Traversal Development by Daniel Kuppitz\u003cbr\u003eExperimental Design by Marko A. Rodriguez\u003cbr\u003eExecutive Producer:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/in/robinmschumacher\"\u003eRobin Schumacher\u003c/a\u003e\u003cbr\u003eUndirected Edge #42 as himself\u003cbr\u003eRussian Language Advisor:\u0026nbsp;\u003ca href=\"https://github.com/xedin\"\u003ePavel Yaskevich\u003c/a\u003e\u003cbr\u003eTamil Language Advisor:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/pub/harihar-shankar/b/747/274\"\u003eHarihar Shankar\u003c/a\u003e\u003cbr\u003eHindi Language Advisor:\u0026nbsp;\u003ca href=\"https://www.linkedin.com/pub/swetha-sharma/13/b62/3b3\"\u003eSwetha Sharma\u003c/a\u003e\u003cbr\u003eInspired by\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy\"\u003eThe Hitchhiker's Guide to the Galaxy\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"https://en.wikipedia.org/wiki/Flatland\"\u003eFlatland\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003eSpecial thanks to\u0026nbsp;\u003ca href=\"https://www.datastax.com/\"\u003eDataStax\u003c/a\u003e\u0026nbsp;and\u0026nbsp;\u003ca href=\"http://tinkerpop.incubator.apache.org/\"\u003eApache TinkerPop\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eNo traversers were harmed during the making of this story.\u003c/p\u003e\n\u003c/div\u003e"])</script><script>self.__next_f.push([1,"a2:{\"cta\":\"$84\",\"title\":\"DataStax AI Platform:\\\\\\\\The Fastest Way to Build and Deploy AI Apps\"}\n"])</script><script>self.__next_f.push([1,"12:[[\"$\",\"header\",null,{\"className\":\"styles_header__sOX2g \",\"children\":[[\"$\",\"$L1f\",null,{\"data\":{\"secondaryMenu\":[{\"_type\":\"cta\",\"text\":\"Docs\",\"_key\":\"3fa43611dc92\",\"url\":\"https://docs.datastax.com/en/home/index.html\"},{\"_type\":\"cta\",\"text\":\"Contact Us\",\"_key\":\"2bfe4775abdf\",\"url\":\"/contact-us\"},{\"url\":\"https://accounts.datastax.com/session-service/v1/login\",\"_type\":\"cta\",\"text\":\"Sign In\",\"_key\":\"54dae1fe8f42\"}],\"buttonsMenu\":[{\"url\":\"https://accounts.datastax.com/session-service/v1/login\",\"_type\":\"cta\",\"text\":\"Sign In\",\"_key\":\"008c0ff3c374\"},{\"url\":\"https://astra.datastax.com/signup?type=langflow\",\"_type\":\"cta\",\"text\":\"Try For Free\",\"_key\":\"537b8e7991e9\"}],\"menu\":[{\"text\":\"Products\",\"_key\":\"d5e2317ece8b\",\"rightBlocks\":[{\"image\":{\"asset\":{\"_ref\":\"image-7fc25f11721699c4b197088a9ec58727513391e7-800x400-png\",\"_type\":\"reference\"},\"_type\":\"altImage\",\"alt\":\"Cassandra Forward 2025\"},\"_type\":\"header.submenu.cta\",\"_key\":\"2bea9e4b8e76\",\"title\":\"Cassandra Forward Is Back!\",\"ctas\":[{\"text\":\"Register Now\",\"_key\":\"e1e0667def13\",\"url\":\"/events/cassandra-forward-march-2025\",\"_type\":\"cta\"}],\"content\":[{\"_type\":\"block\",\"style\":\"normal\",\"_key\":\"682a17a0557f\",\"markDefs\":[],\"children\":[{\"_key\":\"e338dd2a79c0\",\"_type\":\"span\",\"marks\":[\"strong\"],\"text\":\"MARCH 11 (NAM) | MARCH 12 (APAC) | VIRTUAL EVENT\"}]},{\"children\":[{\"_type\":\"span\",\"marks\":[],\"text\":\"Join us for a virtual event showcasing the next generation features of Apache Cassandra®. 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