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vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Software"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Software</span> </div> </a> <ul id="toc-Software-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon 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subtopics</span> </div> </a> <ul id="toc-Specialized_subtopics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Graph drawing</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://es.wikipedia.org/wiki/Dibujo_de_grafos" title="Dibujo de grafos – Spanish" lang="es" hreflang="es" data-title="Dibujo de grafos" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%B3%D9%85_%DA%AF%D8%B1%D8%A7%D9%81" title="رسم گراف – Persian" lang="fa" hreflang="fa" data-title="رسم گراف" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Trac%C3%A9_de_graphes" title="Tracé de graphes – French" lang="fr" hreflang="fr" data-title="Tracé de graphes" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%B8%EB%9E%98%ED%94%84_%EA%B7%B8%EB%A6%AC%EA%B8%B0" title="그래프 그리기 – Korean" lang="ko" hreflang="ko" data-title="그래프 그리기" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Raffigurazione_di_un_grafo" title="Raffigurazione di un grafo – Italian" lang="it" hreflang="it" data-title="Raffigurazione di un grafo" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B8%D0%B7%D1%83%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F_%D0%B3%D1%80%D0%B0%D1%84%D0%BE%D0%B2" title="Визуализация графов – Russian" lang="ru" hreflang="ru" data-title="Визуализация графов" data-language-autonym="Русский" 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Visualization of node-link graphs</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:WorldWideWebAroundWikipedia.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/WorldWideWebAroundWikipedia.png/220px-WorldWideWebAroundWikipedia.png" decoding="async" width="220" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/WorldWideWebAroundWikipedia.png/330px-WorldWideWebAroundWikipedia.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/WorldWideWebAroundWikipedia.png/440px-WorldWideWebAroundWikipedia.png 2x" data-file-width="1185" data-file-height="853" /></a><figcaption>Graphic representation of a minute fraction of the <a href="/wiki/WWW" class="mw-redirect" title="WWW">WWW</a>, demonstrating <a href="/wiki/Hyperlink" title="Hyperlink">hyperlinks</a>.</figcaption></figure> <p><b>Graph drawing</b> is an area of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a> combining methods from <a href="/wiki/Geometric_graph_theory" title="Geometric graph theory">geometric graph theory</a> and <a href="/wiki/Information_visualization" class="mw-redirect" title="Information visualization">information visualization</a> to derive two-dimensional depictions of <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">graphs</a> arising from applications such as <a href="/wiki/Social_network_analysis" title="Social network analysis">social network analysis</a>, <a href="/wiki/Cartography" title="Cartography">cartography</a>, <a href="/wiki/Linguistics" title="Linguistics">linguistics</a>, and <a href="/wiki/Bioinformatics" title="Bioinformatics">bioinformatics</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>A drawing of a graph or <b>network diagram</b> is a pictorial representation of the <a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">vertices</a> and <a href="/wiki/Edge_(graph_theory)" class="mw-redirect" title="Edge (graph theory)">edges</a> of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph.<sup id="cite_ref-dett6_2-0" class="reference"><a href="#cite_note-dett6-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In the abstract, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the arrangement of these vertices and edges within a drawing affects its understandability, usability, fabrication cost, and <a href="/wiki/Aesthetics" title="Aesthetics">aesthetics</a>.<sup id="cite_ref-dett-viii_3-0" class="reference"><a href="#cite_note-dett-viii-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The problem gets worse if the graph changes over time by adding and deleting edges (dynamic graph drawing) and the goal is to preserve the user's mental map.<sup id="cite_ref-FOOTNOTEMisueEadesLaiSugiyama1995_4-0" class="reference"><a href="#cite_note-FOOTNOTEMisueEadesLaiSugiyama1995-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Graphical_conventions">Graphical conventions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=1" title="Edit section: Graphical conventions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:4node-digraph-natural.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/4node-digraph-natural.svg/110px-4node-digraph-natural.svg.png" decoding="async" width="110" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/4node-digraph-natural.svg/165px-4node-digraph-natural.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/4node-digraph-natural.svg/220px-4node-digraph-natural.svg.png 2x" data-file-width="141" data-file-height="146" /></a><figcaption><a href="/wiki/Directed_graph" title="Directed graph">Directed graph</a> with arrowheads showing edge directions</figcaption></figure> <p>Graphs are frequently drawn as node–link diagrams in which the vertices are represented as disks, boxes, or textual labels and the edges are represented as <a href="/wiki/Line_segment" title="Line segment">line segments</a>, <a href="/wiki/Polygonal_chain" title="Polygonal chain">polylines</a>, or curves in the <a href="/wiki/Euclidean_plane" title="Euclidean plane">Euclidean plane</a>.<sup id="cite_ref-dett-viii_3-1" class="reference"><a href="#cite_note-dett-viii-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Node–link diagrams can be traced back to the 14th-16th century works of Pseudo-Lull which were published under the name of <a href="/wiki/Ramon_Llull" title="Ramon Llull">Ramon Llull</a>, a 13th century polymath. Pseudo-Lull drew diagrams of this type for <a href="/wiki/Complete_graph" title="Complete graph">complete graphs</a> in order to analyze all pairwise combinations among sets of metaphysical concepts.<sup id="cite_ref-FOOTNOTEKnuth2013_5-0" class="reference"><a href="#cite_note-FOOTNOTEKnuth2013-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>In the case of <a href="/wiki/Directed_graph" title="Directed graph">directed graphs</a>, <a href="/wiki/Arrow_(symbol)" title="Arrow (symbol)">arrowheads</a> form a commonly used graphical convention to show their <a href="/wiki/Orientability" title="Orientability">orientation</a>;<sup id="cite_ref-dett6_2-1" class="reference"><a href="#cite_note-dett6-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> however, user studies have shown that other conventions such as tapering provide this information more effectively.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Upward_planar_drawing" title="Upward planar drawing">Upward planar drawing</a> uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.<sup id="cite_ref-FOOTNOTEGargTamassia1995_7-0" class="reference"><a href="#cite_note-FOOTNOTEGargTamassia1995-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Alternative conventions to node–link diagrams include adjacency representations such as <a href="/wiki/Circle_packing_theorem" title="Circle packing theorem">circle packings</a>, in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; <a href="/wiki/Intersection_graph" title="Intersection graph">intersection representations</a> in which vertices are represented by non-disjoint geometric objects and edges are represented by their intersections; visibility representations in which vertices are represented by regions in the plane and edges are represented by regions that have an unobstructed line of sight to each other; confluent drawings, in which edges are represented as smooth curves within mathematical <a href="/wiki/Train_track_(mathematics)" title="Train track (mathematics)">train tracks</a>; fabrics, in which nodes are represented as horizontal lines and edges as vertical lines;<sup id="cite_ref-Longabaugh_2012_8-0" class="reference"><a href="#cite_note-Longabaugh_2012-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and visualizations of the <a href="/wiki/Adjacency_matrix" title="Adjacency matrix">adjacency matrix</a> of the graph. </p> <div class="mw-heading mw-heading2"><h2 id="Quality_measures">Quality measures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=2" title="Edit section: Quality measures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many different quality measures have been defined for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In addition to guiding the choice between different layout methods for the same graph, some layout methods attempt to directly optimize these measures. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:4node-digraph-embed.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/4node-digraph-embed.svg/110px-4node-digraph-embed.svg.png" decoding="async" width="110" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/4node-digraph-embed.svg/165px-4node-digraph-embed.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/4node-digraph-embed.svg/220px-4node-digraph-embed.svg.png 2x" data-file-width="141" data-file-height="160" /></a><figcaption><a href="/wiki/Planar_graph" title="Planar graph">Planar graph</a> drawn without overlapping edges</figcaption></figure> <ul><li>The <a href="/wiki/Crossing_number_(graph_theory)" title="Crossing number (graph theory)">crossing number</a> of a drawing is the number of pairs of edges that cross each other. If the graph is <a href="/wiki/Planar_graph" title="Planar graph">planar</a>, then it is often convenient to draw it without any edge intersections; that is, in this case, a graph drawing represents a <a href="/wiki/Graph_embedding" title="Graph embedding">graph embedding</a>. However, nonplanar graphs frequently arise in applications, so graph drawing algorithms must generally allow for edge crossings.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Area_(graph_drawing)" title="Area (graph drawing)">area</a> of a drawing is the size of its smallest <a href="/wiki/Bounding_box" class="mw-redirect" title="Bounding box">bounding box</a>, relative to the closest distance between any two vertices. Drawings with smaller area are generally preferable to those with larger area, because they allow the features of the drawing to be shown at greater size and therefore more legibly. The <a href="/wiki/Aspect_ratio" title="Aspect ratio">aspect ratio</a> of the bounding box may also be important.</li> <li>Symmetry display is the problem of finding <a href="/wiki/Graph_automorphism" title="Graph automorphism">symmetry groups</a> within a given graph, and finding a drawing that displays as much of the symmetry as possible. Some layout methods automatically lead to symmetric drawings; alternatively, some drawing methods start by finding symmetries in the input graph and using them to construct a drawing.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li>It is important that edges have shapes that are as simple as possible, to make it easier for the eye to follow them. In polyline drawings, the complexity of an edge may be measured by its <a href="/wiki/Bend_minimization" title="Bend minimization">number of bends</a>, and many methods aim to provide drawings with few total bends or few bends per edge. Similarly for spline curves the complexity of an edge may be measured by the number of control points on the edge.</li> <li>Several commonly used quality measures concern lengths of edges: it is generally desirable to minimize the total length of the edges as well as the maximum length of any edge. Additionally, it may be preferable for the lengths of edges to be uniform rather than highly varied.</li> <li><a href="/wiki/Angular_resolution_(graph_drawing)" title="Angular resolution (graph drawing)">Angular resolution</a> is a measure of the sharpest angles in a graph drawing. If a graph has vertices with high <a href="/wiki/Degree_(graph_theory)" title="Degree (graph theory)">degree</a> then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree.<sup id="cite_ref-FOOTNOTEPachSharir2009_12-0" class="reference"><a href="#cite_note-FOOTNOTEPachSharir2009-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Slope_number" title="Slope number">slope number</a> of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (allowing crossings). <a href="/wiki/Cubic_graph" title="Cubic graph">Cubic graphs</a> have slope number at most four, but graphs of degree five may have unbounded slope number; it remains open whether the slope number of degree-4 graphs is bounded.<sup id="cite_ref-FOOTNOTEPachSharir2009_12-1" class="reference"><a href="#cite_note-FOOTNOTEPachSharir2009-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Layout_methods">Layout methods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=3" title="Edit section: Layout methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Social_Network_Analysis_Visualization.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Social_Network_Analysis_Visualization.png/220px-Social_Network_Analysis_Visualization.png" decoding="async" width="220" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Social_Network_Analysis_Visualization.png/330px-Social_Network_Analysis_Visualization.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Social_Network_Analysis_Visualization.png/440px-Social_Network_Analysis_Visualization.png 2x" data-file-width="1184" data-file-height="882" /></a><figcaption>A force-based network visualization.<sup id="cite_ref-FOOTNOTEGrandjean2014_13-0" class="reference"><a href="#cite_note-FOOTNOTEGrandjean2014-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Spectral_graph_drawing_of_small_world_graph.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Spectral_graph_drawing_of_small_world_graph.svg/220px-Spectral_graph_drawing_of_small_world_graph.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Spectral_graph_drawing_of_small_world_graph.svg/330px-Spectral_graph_drawing_of_small_world_graph.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Spectral_graph_drawing_of_small_world_graph.svg/440px-Spectral_graph_drawing_of_small_world_graph.svg.png 2x" data-file-width="614" data-file-height="461" /></a><figcaption>Spectral graph layout visualization.</figcaption></figure> <p>There are many different graph layout strategies: </p> <ul><li>In <a href="/wiki/Force-based_layout" class="mw-redirect" title="Force-based layout">force-based layout</a> systems, the graph drawing software modifies an initial vertex placement by continuously moving the vertices according to a system of forces based on physical metaphors related to systems of <a href="/wiki/Spring_(device)" title="Spring (device)">springs</a> or <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">molecular mechanics</a>. Typically, these systems combine attractive forces between adjacent vertices with repulsive forces between all pairs of vertices, in order to seek a layout in which edge lengths are small while vertices are well-separated. These systems may perform <a href="/wiki/Gradient_descent" title="Gradient descent">gradient descent</a> based minimization of an <a href="/wiki/Energy_function" class="mw-redirect" title="Energy function">energy function</a>, or they may translate the forces directly into velocities or accelerations for the moving vertices.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Spectral_layout" title="Spectral layout">Spectral layout</a> methods use as coordinates the <a href="/wiki/Eigenvector" class="mw-redirect" title="Eigenvector">eigenvectors</a> of a <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> such as the <a href="/wiki/Discrete_Laplace_operator" title="Discrete Laplace operator">Laplacian</a> derived from the <a href="/wiki/Adjacency_matrix" title="Adjacency matrix">adjacency matrix</a> of the graph.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li> <li>Orthogonal layout methods, which allow the edges of the graph to run horizontally or vertically, parallel to the coordinate axes of the layout. These methods were originally designed for <a href="/wiki/VLSI" class="mw-redirect" title="VLSI">VLSI</a> and <a href="/wiki/Printed_circuit_board" title="Printed circuit board">PCB</a> layout problems but they have also been adapted for graph drawing. They typically involve a multiphase approach in which an input graph is planarized by replacing crossing points by vertices, a topological embedding of the planarized graph is found, edge orientations are chosen to minimize bends, vertices are placed consistently with these orientations, and finally a layout compaction stage reduces the area of the drawing.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li> <li>Tree layout algorithms these show a rooted <a href="/wiki/Tree_structure" title="Tree structure">tree</a>-like formation, suitable for <a href="/wiki/Tree_(graph_theory)" title="Tree (graph theory)">trees</a>. Often, in a technique called "balloon layout", the children of each node in the tree are drawn on a circle surrounding the node, with the radii of these circles diminishing at lower levels in the tree so that these circles do not overlap.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Layered_graph_drawing" title="Layered graph drawing">Layered graph drawing</a> methods (often called Sugiyama-style drawing) are best suited for <a href="/wiki/Directed_acyclic_graph" title="Directed acyclic graph">directed acyclic graphs</a> or graphs that are nearly acyclic, such as the graphs of dependencies between modules or functions in a software system. In these methods, the nodes of the graph are arranged into horizontal layers using methods such as the <a href="/wiki/Coffman%E2%80%93Graham_algorithm" title="Coffman–Graham algorithm">Coffman–Graham algorithm</a>, in such a way that most edges go downwards from one layer to the next; after this step, the nodes within each layer are arranged in order to minimize crossings.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Goldner-Harary-linear.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Goldner-Harary-linear.svg/220px-Goldner-Harary-linear.svg.png" decoding="async" width="220" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Goldner-Harary-linear.svg/330px-Goldner-Harary-linear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Goldner-Harary-linear.svg/440px-Goldner-Harary-linear.svg.png 2x" data-file-width="432" data-file-height="360" /></a><figcaption>Arc diagram</figcaption></figure> <ul><li><a href="/wiki/Arc_diagram" title="Arc diagram">Arc diagrams</a>, a layout style dating back to the 1960s,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> place vertices on a line; edges may be drawn as semicircles above or below the line, or as smooth curves linked together from multiple semicircles.</li> <li><a href="/wiki/Circular_layout" title="Circular layout">Circular layout</a> methods place the vertices of the graph on a circle, choosing carefully the ordering of the vertices around the circle to reduce crossings and place adjacent vertices close to each other. Edges may be drawn either as chords of the circle or as arcs inside or outside of the circle. In some cases, multiple circles may be used.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Dominance_drawing" title="Dominance drawing">Dominance drawing</a> places vertices in such a way that one vertex is upwards, rightwards, or both of another if and only if it is <a href="/wiki/Reachability" title="Reachability">reachable</a> from the other vertex. In this way, the layout style makes the reachability relation of the graph visually apparent.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Application-specific_graph_drawings">Application-specific graph drawings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=4" title="Edit section: Application-specific graph drawings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Graphs and graph drawings arising in other areas of application include </p> <ul><li><a href="/wiki/Sociogram" title="Sociogram">Sociograms</a>, drawings of a <a href="/wiki/Social_network" title="Social network">social network</a>, as often offered by <a href="/wiki/Social_network_analysis_software" title="Social network analysis software">social network analysis software</a><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Hasse_diagram" title="Hasse diagram">Hasse diagrams</a>, a type of graph drawing specialized to <a href="/wiki/Partial_order" class="mw-redirect" title="Partial order">partial orders</a><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Dessin_d%27enfant" title="Dessin d'enfant">Dessin d'enfants</a>, a type of graph drawing used in <a href="/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a><sup id="cite_ref-FOOTNOTEZapponi2003_24-0" class="reference"><a href="#cite_note-FOOTNOTEZapponi2003-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/State_diagram" title="State diagram">State diagrams</a>, graphical representations of <a href="/wiki/Finite-state_machine" title="Finite-state machine">finite-state machines</a><sup id="cite_ref-FOOTNOTEAndersonHead2006_25-0" class="reference"><a href="#cite_note-FOOTNOTEAndersonHead2006-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Computer_network_diagram" title="Computer network diagram">Computer network diagrams</a>, depictions of the nodes and connections in a <a href="/wiki/Computer_network" title="Computer network">computer network</a><sup id="cite_ref-FOOTNOTEDi_BattistaRimondini2014_26-0" class="reference"><a href="#cite_note-FOOTNOTEDi_BattistaRimondini2014-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Flowchart" title="Flowchart">Flowcharts</a> and <a href="/wiki/DRAKON" title="DRAKON">drakon-charts</a>, drawings in which the nodes represent the steps of an <a href="/wiki/Algorithm" title="Algorithm">algorithm</a> and the edges represent <a href="/wiki/Control_flow" title="Control flow">control flow</a> between steps.</li> <li><a href="/wiki/Data-flow_diagram" title="Data-flow diagram">Data-flow diagrams</a>, drawings in which the nodes represent the components of an <a href="/wiki/Information_system" title="Information system">information system</a> and the edges represent the movement of information from one component to another.</li> <li><a href="/wiki/Bioinformatics" title="Bioinformatics">Bioinformatics</a> including <a href="/wiki/Phylogenetic_tree" title="Phylogenetic tree">phylogenetic trees</a>, <a href="/wiki/Protein%E2%80%93protein_interaction" title="Protein–protein interaction">protein–protein interaction</a> networks, and <a href="/wiki/Metabolic_pathway" title="Metabolic pathway">metabolic pathways</a>.<sup id="cite_ref-FOOTNOTEBachmaierBrandesSchreiber2014_27-0" class="reference"><a href="#cite_note-FOOTNOTEBachmaierBrandesSchreiber2014-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li></ul> <p>In addition, the <a href="/wiki/Placement_(electronic_design_automation)" title="Placement (electronic design automation)">placement</a> and <a href="/wiki/Routing_(electronic_design_automation)" title="Routing (electronic design automation)">routing</a> steps of <a href="/wiki/Electronic_design_automation" title="Electronic design automation">electronic design automation</a> (EDA) are similar in many ways to graph drawing, as is the problem of <a href="/wiki/Greedy_embedding" title="Greedy embedding">greedy embedding</a> in <a href="/wiki/Distributed_computing" title="Distributed computing">distributed computing</a>, and the graph drawing literature includes several results borrowed from the EDA literature. However, these problems also differ in several important ways: for instance, in EDA, area minimization and signal length are more important than aesthetics, and the routing problem in EDA may have more than two terminals per net while the analogous problem in graph drawing generally only involves pairs of vertices for each edge. </p> <div class="mw-heading mw-heading2"><h2 id="Software">Software</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=5" title="Edit section: Software"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png/220px-Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png" decoding="async" width="220" height="137" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png/330px-Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png/440px-Gephi_0.9.1_Network_Analysis_and_Visualization_Software.png 2x" data-file-width="1397" data-file-height="871" /></a><figcaption>A graph drawing interface (<a href="/wiki/Gephi" title="Gephi">Gephi</a> 0.9.1)</figcaption></figure><p>Software, systems, and providers of systems for drawing graphs include: </p><ul><li><a href="/wiki/BioFabric" title="BioFabric">BioFabric</a> open-source software for visualizing large networks by drawing nodes as horizontal lines.</li> <li><a href="/wiki/Cytoscape" title="Cytoscape">Cytoscape</a>, open-source software for visualizing molecular interaction networks</li> <li><a href="/wiki/Gephi" title="Gephi">Gephi</a>, open-source network analysis and visualization software</li> <li><a href="/wiki/Graph-tool" title="Graph-tool">graph-tool</a>, a <a href="/wiki/Free_Software" class="mw-redirect" title="Free Software">free/libre</a> <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> library for analysis of graphs</li> <li><a href="/wiki/Graphviz" title="Graphviz">Graphviz</a>, an open-source graph drawing system from <a href="/wiki/AT%26T_Corporation" title="AT&T Corporation">AT&T Corporation</a><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Linkurious" title="Linkurious">Linkurious</a>, a commercial network analysis and visualization software for <a href="/wiki/Graph_databases" class="mw-redirect" title="Graph databases">graph databases</a></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a>, a general-purpose computation tool that includes 2D and 3D graph visualization and graph analysis tools.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Microsoft_Automatic_Graph_Layout" title="Microsoft Automatic Graph Layout">Microsoft Automatic Graph Layout</a>, open-source .NET library (formerly called GLEE) for laying out graphs<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/NetworkX" title="NetworkX">NetworkX</a> is a Python library for studying graphs and networks.</li> <li><a href="/wiki/Tulip_(software)" title="Tulip (software)">Tulip</a>,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> an open-source data visualization tool</li> <li><a href="/wiki/YEd" title="YEd">yEd</a>, a graph editor with graph layout functionality<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/PGF/TikZ" title="PGF/TikZ">PGF/TikZ</a> 3.0 with the <code>graphdrawing</code> package (requires <a href="/wiki/LuaTeX" title="LuaTeX">LuaTeX</a>).<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/LaNet-vi" title="LaNet-vi">LaNet-vi</a>, an open-source large network visualization software</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/International_Symposium_on_Graph_Drawing" title="International Symposium on Graph Drawing">International Symposium on Graph Drawing</a></li> <li><a href="/wiki/List_of_Unified_Modeling_Language_tools" title="List of Unified Modeling Language tools">List of Unified Modeling Language tools</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Footnotes">Footnotes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=8" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, pp. vii–viii; <a href="#CITEREFHermanMelançonMarshall2000">Herman, Melançon & Marshall (2000)</a>, Section 1.1, "Typical Application Areas".</span> </li> <li id="cite_note-dett6-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-dett6_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-dett6_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, p. 6.</span> </li> <li id="cite_note-dett-viii-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-dett-viii_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-dett-viii_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, p. viii.</span> </li> <li id="cite_note-FOOTNOTEMisueEadesLaiSugiyama1995-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMisueEadesLaiSugiyama1995_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMisueEadesLaiSugiyama1995">Misue et al. (1995)</a>.</span> </li> <li id="cite_note-FOOTNOTEKnuth2013-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKnuth2013_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKnuth2013">Knuth (2013)</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="#CITEREFHoltenvan_Wijk2009">Holten & van Wijk (2009)</a>; <a href="#CITEREFHoltenIsenbergvan_WijkFekete2011">Holten et al. (2011)</a>.</span> </li> <li id="cite_note-FOOTNOTEGargTamassia1995-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGargTamassia1995_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGargTamassia1995">Garg & Tamassia (1995)</a>.</span> </li> <li id="cite_note-Longabaugh_2012-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Longabaugh_2012_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLongabaugh2012">Longabaugh (2012)</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, Section 2.1.2, Aesthetics, pp. 14–16; <a href="#CITEREFPurchaseCohenJames1997">Purchase, Cohen & James (1997)</a>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, p 14.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, p. 16.</span> </li> <li id="cite_note-FOOTNOTEPachSharir2009-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEPachSharir2009_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEPachSharir2009_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFPachSharir2009">Pach & Sharir (2009)</a>.</span> </li> <li id="cite_note-FOOTNOTEGrandjean2014-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGrandjean2014_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGrandjean2014">Grandjean (2014)</a>.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a href="#CITEREFBeckman1994">Beckman (1994)</a>; <a href="#CITEREFKoren2005">Koren (2005)</a>.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; <a href="#CITEREFEiglspergerFeketeKlau2001">Eiglsperger, Fekete & Klau (2001)</a>.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><a href="#CITEREFHermanMelançonMarshall2000">Herman, Melançon & Marshall (2000)</a>, Section 2.2, "Traditional Layout – An Overview".</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><a href="#CITEREFSugiyamaTagawaToda1981">Sugiyama, Tagawa & Toda (1981)</a>; <a href="#CITEREFBastertMatuszewski2001">Bastert & Matuszewski (2001)</a>; <a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><a href="#CITEREFSaaty1964">Saaty (1964)</a>.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><a href="#CITEREFDoğrusözMaddenMadden1997">Doğrusöz, Madden & Madden (1997)</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, Section 4.7, "Dominance Drawings", pp. 112–127.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><a href="#CITEREFScott2000">Scott (2000)</a>; <a href="#CITEREFBrandesFreemanWagner2014">Brandes, Freeman & Wagner (2014)</a>.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaEadesTamassiaTollis1998">Di Battista et al. (1998)</a>, pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; <a href="#CITEREFFreese2004">Freese (2004)</a>.</span> </li> <li id="cite_note-FOOTNOTEZapponi2003-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEZapponi2003_24-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFZapponi2003">Zapponi (2003)</a>.</span> </li> <li id="cite_note-FOOTNOTEAndersonHead2006-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEAndersonHead2006_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAndersonHead2006">Anderson & Head (2006)</a>.</span> </li> <li id="cite_note-FOOTNOTEDi_BattistaRimondini2014-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDi_BattistaRimondini2014_26-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDi_BattistaRimondini2014">Di Battista & Rimondini (2014)</a>.</span> </li> <li id="cite_note-FOOTNOTEBachmaierBrandesSchreiber2014-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBachmaierBrandesSchreiber2014_27-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBachmaierBrandesSchreiber2014">Bachmaier, Brandes & Schreiber (2014)</a>.</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">"Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in <a href="#CITEREFJüngerMutzel2004">Jünger & Mutzel (2004)</a>.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://reference.wolfram.com/mathematica/tutorial/GraphDrawingIntroduction.html">"Introduction to graph drawing"</a>, <i>Wolfram Language & System Documentation Center</i><span class="reference-accessdate">, retrieved <span class="nowrap">2024-03-21</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wolfram+Language+%26+System+Documentation+Center&rft.atitle=Introduction+to+graph+drawing&rft_id=http%3A%2F%2Freference.wolfram.com%2Fmathematica%2Ftutorial%2FGraphDrawingIntroduction.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><a href="#CITEREFNachmansonRobertsonLee2008">Nachmanson, Robertson & Lee (2008)</a>.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text">"Tulip – A Huge Graph Visualization Framework", by David Auber, in <a href="#CITEREFJüngerMutzel2004">Jünger & Mutzel (2004)</a>.</span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text">"yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in <a href="#CITEREFJüngerMutzel2004">Jünger & Mutzel (2004)</a>.</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><a href="#CITEREFTantau2013">Tantau (2013)</a>; see also the older <a rel="nofollow" class="external text" href="http://www.tcs.uni-luebeck.de/downloads/mitarbeiter/tantau/2012-gd-presentation.pdf">GD 2012 presentation</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160527034523/http://www.tcs.uni-luebeck.de/downloads/mitarbeiter/tantau/2012-gd-presentation.pdf">Archived</a> 2016-05-27 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="General_references">General references</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=9" title="Edit section: General references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDi_BattistaEadesTamassiaTollis1998" class="citation cs2">Di Battista, Giuseppe; <a href="/wiki/Peter_Eades" title="Peter Eades">Eades, Peter</a>; <a href="/wiki/Roberto_Tamassia" title="Roberto Tamassia">Tamassia, Roberto</a>; Tollis, Ioannis G. (1998), <i>Graph Drawing: Algorithms for the Visualization of Graphs</i>, <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-301615-4" title="Special:BookSources/978-0-13-301615-4"><bdi>978-0-13-301615-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Graph+Drawing%3A+Algorithms+for+the+Visualization+of+Graphs&rft.pub=Prentice+Hall&rft.date=1998&rft.isbn=978-0-13-301615-4&rft.aulast=Di+Battista&rft.aufirst=Giuseppe&rft.au=Eades%2C+Peter&rft.au=Tamassia%2C+Roberto&rft.au=Tollis%2C+Ioannis+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHermanMelançonMarshall2000" class="citation cs2">Herman, Ivan; Melançon, Guy; Marshall, M. Scott (2000), "Graph Visualization and Navigation in Information Visualization: A Survey", <i>IEEE Transactions on Visualization and Computer Graphics</i>, <b>6</b> (1): 24–43, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F2945.841119">10.1109/2945.841119</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Visualization+and+Computer+Graphics&rft.atitle=Graph+Visualization+and+Navigation+in+Information+Visualization%3A+A+Survey&rft.volume=6&rft.issue=1&rft.pages=24-43&rft.date=2000&rft_id=info%3Adoi%2F10.1109%2F2945.841119&rft.aulast=Herman&rft.aufirst=Ivan&rft.au=Melan%C3%A7on%2C+Guy&rft.au=Marshall%2C+M.+Scott&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJüngerMutzel2004" class="citation cs2">Jünger, Michael; <a href="/wiki/Petra_Mutzel" title="Petra Mutzel">Mutzel, Petra</a> (2004), <i>Graph Drawing Software</i>, Springer-Verlag, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-00881-1" title="Special:BookSources/978-3-540-00881-1"><bdi>978-3-540-00881-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Graph+Drawing+Software&rft.pub=Springer-Verlag&rft.date=2004&rft.isbn=978-3-540-00881-1&rft.aulast=J%C3%BCnger&rft.aufirst=Michael&rft.au=Mutzel%2C+Petra&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Specialized_subtopics">Specialized subtopics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=10" title="Edit section: Specialized subtopics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316"><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAndersonHead2006" class="citation cs2">Anderson, James Andrew; Head, Thomas J. (2006), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ikS8BLdLDxIC&pg=PA38"><i>Automata Theory with Modern Applications</i></a>, Cambridge University Press, pp. 38–41, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-84887-9" title="Special:BookSources/978-0-521-84887-9"><bdi>978-0-521-84887-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Automata+Theory+with+Modern+Applications&rft.pages=38-41&rft.pub=Cambridge+University+Press&rft.date=2006&rft.isbn=978-0-521-84887-9&rft.aulast=Anderson&rft.aufirst=James+Andrew&rft.au=Head%2C+Thomas+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DikS8BLdLDxIC%26pg%3DPA38&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBachmaierBrandesSchreiber2014" class="citation cs2">Bachmaier, Christian; <a href="/wiki/Ulrik_Brandes" title="Ulrik Brandes">Brandes, Ulrik</a>; Schreiber, Falk (2014), "Biological Networks", in <a href="/wiki/Roberto_Tamassia" title="Roberto Tamassia">Tamassia, Roberto</a> (ed.), <i>Handbook of Graph Drawing and Visualization</i>, CRC Press, pp. 621–651</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Biological+Networks&rft.btitle=Handbook+of+Graph+Drawing+and+Visualization&rft.pages=621-651&rft.pub=CRC+Press&rft.date=2014&rft.aulast=Bachmaier&rft.aufirst=Christian&rft.au=Brandes%2C+Ulrik&rft.au=Schreiber%2C+Falk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBastertMatuszewski2001" class="citation cs2">Bastert, Oliver; Matuszewski, Christian (2001), "Layered drawings of digraphs", in Kaufmann, Michael; <a href="/wiki/Dorothea_Wagner" title="Dorothea Wagner">Wagner, Dorothea</a> (eds.), <i>Drawing Graphs: Methods and Models</i>, Lecture Notes in Computer Science, vol. 2025, Springer-Verlag, pp. 87–120, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-44969-8_5">10.1007/3-540-44969-8_5</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-42062-0" title="Special:BookSources/978-3-540-42062-0"><bdi>978-3-540-42062-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Layered+drawings+of+digraphs&rft.btitle=Drawing+Graphs%3A+Methods+and+Models&rft.series=Lecture+Notes+in+Computer+Science&rft.pages=87-120&rft.pub=Springer-Verlag&rft.date=2001&rft_id=info%3Adoi%2F10.1007%2F3-540-44969-8_5&rft.isbn=978-3-540-42062-0&rft.aulast=Bastert&rft.aufirst=Oliver&rft.au=Matuszewski%2C+Christian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeckman1994" class="citation cs2">Beckman, Brian (1994), <a rel="nofollow" class="external text" href="http://research.microsoft.com/apps/pubs/default.aspx?id=69611"><i>Theory of Spectral Graph Layout</i></a>, Tech. 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Saaty">Saaty, Thomas L.</a> (1964), <a rel="nofollow" class="external text" href="https://www.pnas.org/doi/abs/10.1073/pnas.52.3.688">"The minimum number of intersections in complete graphs"</a>, <i>Proc. Natl. Acad. Sci. U.S.A.</i>, <b>52</b> (3): 688–690, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1964PNAS...52..688S">1964PNAS...52..688S</a></span>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.52.3.688">10.1073/pnas.52.3.688</a></span>, <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC300329">300329</a></span>, <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16591215">16591215</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Natl.+Acad.+Sci.+U.S.A.&rft.atitle=The+minimum+number+of+intersections+in+complete+graphs&rft.volume=52&rft.issue=3&rft.pages=688-690&rft.date=1964&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC300329%23id-name%3DPMC&rft_id=info%3Apmid%2F16591215&rft_id=info%3Adoi%2F10.1073%2Fpnas.52.3.688&rft_id=info%3Abibcode%2F1964PNAS...52..688S&rft.aulast=Saaty&rft.aufirst=Thomas+L.&rft_id=https%3A%2F%2Fwww.pnas.org%2Fdoi%2Fabs%2F10.1073%2Fpnas.52.3.688&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScott2000" class="citation cs2">Scott, John (2000), "Sociograms and Graph Theory", <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Ww3_bKcz6kgC&pg=PA"><i>Social network analysis: a handbook</i></a> (2nd ed.), Sage, pp. 64–69, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7619-6339-4" title="Special:BookSources/978-0-7619-6339-4"><bdi>978-0-7619-6339-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Sociograms+and+Graph+Theory&rft.btitle=Social+network+analysis%3A+a+handbook&rft.pages=64-69&rft.edition=2nd&rft.pub=Sage&rft.date=2000&rft.isbn=978-0-7619-6339-4&rft.aulast=Scott&rft.aufirst=John&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWw3_bKcz6kgC%26pg%3DPA&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSugiyamaTagawaToda1981" class="citation cs2 cs1-prop-long-vol"><a href="/wiki/Kozo_Sugiyama" title="Kozo Sugiyama">Sugiyama, Kozo</a>; Tagawa, Shôjirô; Toda, Mitsuhiko (1981), "Methods for visual understanding of hierarchical system structures", <i><a href="/wiki/IEEE_Systems,_Man,_and_Cybernetics_Society" title="IEEE Systems, Man, and Cybernetics Society">IEEE Transactions on Systems, Man, and Cybernetics</a></i>, SMC-11 (2): 109–125, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTSMC.1981.4308636">10.1109/TSMC.1981.4308636</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0611436">0611436</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:8367756">8367756</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Systems%2C+Man%2C+and+Cybernetics&rft.atitle=Methods+for+visual+understanding+of+hierarchical+system+structures&rft.volume=SMC-11&rft.issue=2&rft.pages=109-125&rft.date=1981&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0611436%23id-name%3DMR&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A8367756%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FTSMC.1981.4308636&rft.aulast=Sugiyama&rft.aufirst=Kozo&rft.au=Tagawa%2C+Sh%C3%B4jir%C3%B4&rft.au=Toda%2C+Mitsuhiko&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTantau2013" class="citation cs2">Tantau, Till (2013), "Graph Drawing in TikZ", <i><a href="/wiki/Journal_of_Graph_Algorithms_and_Applications" title="Journal of Graph Algorithms and Applications">Journal of Graph Algorithms and Applications</a></i>, <b>17</b> (4): 495–513, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.7155%2Fjgaa.00301">10.7155/jgaa.00301</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Graph+Algorithms+and+Applications&rft.atitle=Graph+Drawing+in+TikZ&rft.volume=17&rft.issue=4&rft.pages=495-513&rft.date=2013&rft_id=info%3Adoi%2F10.7155%2Fjgaa.00301&rft.aulast=Tantau&rft.aufirst=Till&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZapponi2003" class="citation cs2">Zapponi, Leonardo (August 2003), <a rel="nofollow" class="external text" href="https://www.ams.org/notices/200307/what-is.pdf">"What is a Dessin d'Enfant"</a> <span class="cs1-format">(PDF)</span>, <i><a href="/wiki/Notices_of_the_American_Mathematical_Society" title="Notices of the American Mathematical Society">Notices of the American Mathematical Society</a></i>, <b>50</b>: 788–789, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211003075615/https://www.ams.org/notices/200307/what-is.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 2021-10-03<span class="reference-accessdate">, retrieved <span class="nowrap">2021-04-28</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+American+Mathematical+Society&rft.atitle=What+is+a+Dessin+d%27Enfant&rft.volume=50&rft.pages=788-789&rft.date=2003-08&rft.aulast=Zapponi&rft.aufirst=Leonardo&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200307%2Fwhat-is.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=11" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316"><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDi_BattistaEadesTamassiaTollis1994" class="citation cs2">Di Battista, Giuseppe; <a href="/wiki/Peter_Eades" title="Peter Eades">Eades, Peter</a>; <a href="/wiki/Roberto_Tamassia" title="Roberto Tamassia">Tamassia, Roberto</a>; Tollis, Ioannis G. (1994), "Algorithms for Drawing Graphs: an Annotated Bibliography", <i><a href="/wiki/Computational_Geometry_(journal)" title="Computational Geometry (journal)">Computational Geometry: Theory and Applications</a></i>, <b>4</b> (5): 235–282, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0925-7721%2894%2900014-x">10.1016/0925-7721(94)00014-x</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computational+Geometry%3A+Theory+and+Applications&rft.atitle=Algorithms+for+Drawing+Graphs%3A+an+Annotated+Bibliography&rft.volume=4&rft.issue=5&rft.pages=235-282&rft.date=1994&rft_id=info%3Adoi%2F10.1016%2F0925-7721%2894%2900014-x&rft.aulast=Di+Battista&rft.aufirst=Giuseppe&rft.au=Eades%2C+Peter&rft.au=Tamassia%2C+Roberto&rft.au=Tollis%2C+Ioannis+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaufmannWagner2001" class="citation cs2">Kaufmann, Michael; <a href="/wiki/Dorothea_Wagner" title="Dorothea Wagner">Wagner, Dorothea</a>, eds. (2001), <i>Drawing Graphs: Methods and Models</i>, <a href="/wiki/Lecture_Notes_in_Computer_Science" title="Lecture Notes in Computer Science">Lecture Notes in Computer Science</a>, vol. 2025, Springer-Verlag, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-540-44969-8">10.1007/3-540-44969-8</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-42062-0" title="Special:BookSources/978-3-540-42062-0"><bdi>978-3-540-42062-0</bdi></a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1808286">1808286</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Drawing+Graphs%3A+Methods+and+Models&rft.series=Lecture+Notes+in+Computer+Science&rft.pub=Springer-Verlag&rft.date=2001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1808286%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F3-540-44969-8&rft.isbn=978-3-540-42062-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTamassia2014" class="citation cs2"><a href="/wiki/Roberto_Tamassia" title="Roberto Tamassia">Tamassia, Roberto</a>, ed. (2014), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130815181243/http://cs.brown.edu/~rt/gdhandbook/"><i>Handbook of Graph Drawing and Visualization</i></a>, CRC Press, archived from <a rel="nofollow" class="external text" href="http://cs.brown.edu/~rt/gdhandbook/">the original</a> on 2013-08-15<span class="reference-accessdate">, retrieved <span class="nowrap">2013-08-28</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Graph+Drawing+and+Visualization&rft.pub=CRC+Press&rft.date=2014&rft_id=http%3A%2F%2Fcs.brown.edu%2F~rt%2Fgdhandbook%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGraph+drawing" class="Z3988"></span>.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Graph_drawing&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://graphx.codeplex.com">GraphX library for .NET</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180126071742/http://graphx.codeplex.com/">Archived</a> 2018-01-26 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>: open-source WPF library for graph calculation and visualization. Supports many layout and edge routing algorithms.</li> <li><a rel="nofollow" class="external text" href="http://gdea.informatik.uni-koeln.de/">Graph drawing e-print archive</a>: including information on papers from all <a href="/wiki/International_Symposium_on_Graph_Drawing" title="International Symposium on Graph Drawing">Graph Drawing symposia</a>.</li></ul> <pre>for many additional links related to graph drawing. </pre> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Graph_representations" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Graph_representations" title="Template:Graph representations"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Graph_representations" title="Template talk:Graph representations"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Graph_representations" title="Special:EditPage/Template:Graph representations"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Graph_representations" style="font-size:114%;margin:0 4em">Graph representations</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Data structures</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Graph_(abstract_data_type)" title="Graph (abstract data type)">Graph (abstract data type)</a></li> <li><a href="/wiki/Adjacency_list" title="Adjacency list">Adjacency list</a></li> <li><a href="/wiki/Edge_list" title="Edge list">Edge list</a></li> <li><a href="/wiki/Adjacency_matrix" title="Adjacency matrix">Adjacency matrix</a></li> <li><a href="/wiki/Incidence_matrix" title="Incidence matrix">Incidence matrix</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">XML-based formats</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/DGML" title="DGML">DGML</a></li> <li>DotML</li> <li>GEXF</li> <li><a href="/wiki/GraphML" title="GraphML">GraphML</a></li> <li><a href="/wiki/GXL" title="GXL">GXL</a></li> <li><a href="/wiki/XGMML" title="XGMML">XGMML</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Text-based formats</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/DOT_(graph_description_language)" title="DOT (graph description language)">DOT</a></li> <li><a href="/wiki/Graph_Modelling_Language" title="Graph Modelling Language">Graph Modelling Language</a> (GML)</li> <li><a href="/wiki/LCF_notation" title="LCF notation">LCF notation</a> for cubic Hamiltonian graphs</li> <li><a href="/wiki/Newick_format" title="Newick format">Newick format</a> for trees</li> <li><a href="/wiki/Trivial_Graph_Format" title="Trivial Graph Format">Trivial Graph Format</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Graph_database" title="Graph database">Graph database</a></li> <li><a class="mw-selflink selflink">Graph drawing</a></li> <li><a href="/wiki/Linked_data" title="Linked data">Linked data</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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