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id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Complex network</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://de.wikipedia.org/wiki/Komplexes_Netzwerk" title="Komplexes Netzwerk – German" lang="de" hreflang="de" data-title="Komplexes Netzwerk" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Red_compleja" title="Red compleja – Spanish" lang="es" hreflang="es" data-title="Red compleja" 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%B4%D8%A8%DA%A9%D9%87_%D9%BE%DB%8C%DA%86%DB%8C%D8%AF%D9%87" title="شبکه پیچیده – Persian" lang="fa" hreflang="fa" data-title="شبکه پیچیده" 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/R%C3%A9seau_complexe" title="Réseau complexe – French" lang="fr" hreflang="fr" data-title="Réseau complexe" 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/%EB%B3%B5%EC%9E%A1%EA%B3%84_%EB%84%A4%ED%8A%B8%EC%9B%8C%ED%81%AC" title="복잡계 네트워크 – Korean" lang="ko" hreflang="ko" data-title="복잡계 네트워크" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%A9%D7%AA_%D7%9E%D7%95%D7%A8%D7%9B%D7%91%D7%AA" title="רשת מורכבת – Hebrew" lang="he" hreflang="he" data-title="רשת מורכבת" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Komplex_h%C3%A1l%C3%B3zat" title="Komplex hálózat – Hungarian" lang="hu" hreflang="hu" data-title="Komplex hálózat" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%B6%E0%A5%8D%E0%A4%B0_%E0%A4%9C%E0%A4%BE%E0%A4%B2" title="व्यामिश्र जाल – Marathi" lang="mr" hreflang="mr" data-title="व्यामिश्र जाल" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Complexe_netwerken" title="Complexe netwerken – Dutch" lang="nl" hreflang="nl" data-title="Complexe netwerken" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A4%87%E9%9B%91%E3%83%8D%E3%83%83%E3%83%88%E3%83%AF%E3%83%BC%E3%82%AF" title="複雑ネットワーク – Japanese" lang="ja" hreflang="ja" data-title="複雑ネットワーク" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sie%C4%87_z%C5%82o%C5%BCona" title="Sieć złożona – Polish" lang="pl" hreflang="pl" data-title="Sieć złożona" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_das_redes_complexas" title="Teoria das redes complexas – Portuguese" lang="pt" hreflang="pt" data-title="Teoria das redes complexas" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D1%8B%D0%B5_%D1%81%D0%B5%D1%82%D0%B8" title="Комплексные сети – Russian" lang="ru" hreflang="ru" data-title="Комплексные сети" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Karma%C5%9F%C4%B1k_a%C4%9F" title="Karmaşık ağ – Turkish" lang="tr" hreflang="tr" data-title="Karmaşık ağ" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li 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.sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle" style="padding-bottom:0.15em;">Part of <a href="/wiki/Category:Network_science" title="Category:Network science">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle" style="font-size:175%;"><a href="/wiki/Network_science" title="Network science">Network science</a></th></tr><tr><td class="sidebar-image"><div class="center"><div class="center"> <div style="width: 250px; height: 250px; overflow: hidden;"> <div style="position: relative; top: -0px; left: -0px; width: 250px"><div class="noresize"><span typeof="mw:File"><a href="/wiki/File:Internet_map_1024.jpg" class="mw-file-description"><img alt="Internet_map_1024.jpg" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Internet_map_1024.jpg/250px-Internet_map_1024.jpg" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Internet_map_1024.jpg/375px-Internet_map_1024.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Internet_map_1024.jpg/500px-Internet_map_1024.jpg 2x" data-file-width="1280" data-file-height="1280" /></a></span></div></div> </div> </div></div></td></tr><tr><th class="sidebar-heading"> <div class="hlist"><ul><li><a href="/wiki/Network_theory" title="Network theory">Theory</a></li></ul></div></th></tr><tr><td class="sidebar-content hlist" style="padding-top:0.2em;padding-bottom:0.5em;"> <ul><li><a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">Graph</a></li> <li><a class="mw-selflink selflink">Complex network</a></li> <li><a href="/wiki/Complex_contagion" title="Complex contagion">Contagion</a></li> <li><a href="/wiki/Small-world_network" title="Small-world network">Small-world</a></li> <li><a href="/wiki/Scale-free_network" title="Scale-free network">Scale-free</a></li> <li><a href="/wiki/Community_structure" title="Community structure">Community structure</a></li> <li><a href="/wiki/Percolation_theory" title="Percolation theory">Percolation</a></li> <li><a href="/wiki/Evolving_networks" class="mw-redirect" title="Evolving networks">Evolution</a></li> <li><a href="/wiki/Network_controllability" title="Network controllability">Controllability</a></li> <li><a href="/wiki/Graph_drawing" title="Graph drawing">Graph drawing</a></li> <li><a href="/wiki/Social_capital" title="Social capital">Social capital</a></li> <li><a href="/wiki/Link_analysis" title="Link analysis">Link analysis</a></li> <li><a href="/wiki/Combinatorial_optimization" title="Combinatorial optimization">Optimization</a></li> <li><a href="/wiki/Reciprocity_(network_science)" title="Reciprocity (network science)">Reciprocity</a></li> <li><a href="/wiki/Triadic_closure" title="Triadic closure">Closure</a></li> <li><a href="/wiki/Homophily" title="Homophily">Homophily</a></li> <li><a href="/wiki/Transitive_relation" title="Transitive relation">Transitivity</a></li> <li><a href="/wiki/Preferential_attachment" title="Preferential attachment">Preferential attachment</a></li> <li><a href="/wiki/Balance_theory" title="Balance theory">Balance theory</a></li> <li><a href="/wiki/Network_effect" title="Network effect">Network effect</a></li> <li><a href="/wiki/Social_influence" title="Social influence">Social influence</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Network types</th></tr><tr><td class="sidebar-content hlist" style="padding-top:0.2em;padding-bottom:0.5em;"> <ul><li><a href="/wiki/Computer_network" title="Computer network">Informational (computing)</a></li> <li><a href="/wiki/Telecommunications_network" title="Telecommunications network">Telecommunication</a></li> <li><a href="/wiki/Transport_network" class="mw-redirect" title="Transport network">Transport</a></li> <li><a href="/wiki/Social_network" title="Social network">Social</a></li> <li><a href="/wiki/Scientific_collaboration_network" title="Scientific collaboration network">Scientific collaboration</a></li> <li><a href="/wiki/Biological_network" title="Biological network">Biological</a></li> <li><a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural</a></li> <li><a href="/wiki/Interdependent_networks" title="Interdependent networks">Interdependent</a></li> <li><a href="/wiki/Semantic_network" title="Semantic network">Semantic</a></li> <li><a href="/wiki/Spatial_network" title="Spatial network">Spatial</a></li> <li><a href="/wiki/Dependency_network" title="Dependency network">Dependency</a></li> <li><a href="/wiki/Flow_network" title="Flow network">Flow</a></li> <li><a href="/wiki/Network_on_a_chip" title="Network on a chip">on-Chip</a></li></ul></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">Graphs</a></th></tr><tr><td class="sidebar-content hlist" style="padding-top:0.2em;padding-bottom:0.5em;"> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Features</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Clique_(graph_theory)" title="Clique (graph theory)">Clique</a></li> <li><a href="/wiki/Connected_component_(graph_theory)" class="mw-redirect" title="Connected component (graph theory)">Component</a></li> <li><a href="/wiki/Cut_(graph_theory)" title="Cut (graph theory)">Cut</a></li> <li><a href="/wiki/Cycle_(graph_theory)" title="Cycle (graph theory)">Cycle</a></li> <li><a href="/wiki/Graph_(abstract_data_type)" title="Graph (abstract data type)">Data structure</a></li> <li><a href="/wiki/Edge_(graph_theory)" class="mw-redirect" title="Edge (graph theory)">Edge</a></li> <li><a href="/wiki/Loop_(graph_theory)" title="Loop (graph theory)">Loop</a></li> <li><a href="/wiki/Neighbourhood_(graph_theory)" title="Neighbourhood (graph theory)">Neighborhood</a></li> <li><a href="/wiki/Path_(graph_theory)" title="Path (graph theory)">Path</a></li> <li><a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">Vertex</a></li> <li><span class="nowrap"><a href="/wiki/Adjacency_list" title="Adjacency list">Adjacency list</a> / <a href="/wiki/Adjacency_matrix" title="Adjacency matrix">matrix</a></span></li> <li><span class="nowrap"><a href="/wiki/Incidence_list" class="mw-redirect" title="Incidence list">Incidence list</a> / <a href="/wiki/Incidence_matrix" title="Incidence matrix">matrix</a></span></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Types</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Bipartite_graph" title="Bipartite graph">Bipartite</a></li> <li><a href="/wiki/Complete_graph" title="Complete graph">Complete</a></li> <li><a href="/wiki/Directed_graph" title="Directed graph">Directed</a></li> <li><a href="/wiki/Hypergraph" title="Hypergraph">Hyper</a></li> <li><a href="/wiki/Labeled_graph" class="mw-redirect" title="Labeled graph">Labeled</a></li> <li><a href="/wiki/Multigraph" title="Multigraph">Multi</a></li> <li><a href="/wiki/Random_graph" title="Random graph">Random</a></li> <li><a href="/wiki/Weighted_graph" class="mw-redirect" title="Weighted graph">Weighted</a></li></ul></td> </tr></tbody></table></td> </tr><tr><th class="sidebar-heading"> <div class="hlist"><ul><li><a href="/wiki/Metrics_(networking)" title="Metrics (networking)">Metrics</a></li><li><a href="/wiki/List_of_algorithms#Networking" title="List of algorithms">Algorithms</a></li></ul></div></th></tr><tr><td class="sidebar-content hlist" style="padding-top:0.2em;padding-bottom:0.5em;"> <ul><li><a href="/wiki/Centrality" title="Centrality">Centrality</a></li> <li><a href="/wiki/Degree_(graph_theory)" title="Degree (graph theory)">Degree</a></li> <li><a href="/wiki/Network_motif" title="Network motif">Motif</a></li> <li><a href="/wiki/Clustering_coefficient" title="Clustering coefficient">Clustering</a></li> <li><a href="/wiki/Degree_distribution" title="Degree distribution">Degree distribution</a></li> <li><a href="/wiki/Assortativity" title="Assortativity">Assortativity</a></li> <li><a href="/wiki/Distance_(graph_theory)" title="Distance (graph theory)">Distance</a></li> <li><a href="/wiki/Modularity_(networks)" title="Modularity (networks)">Modularity</a></li> <li><a href="/wiki/Efficiency_(network_science)" title="Efficiency (network science)">Efficiency</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Models</th></tr><tr><td class="sidebar-content hlist" style="padding-top:0.2em;padding-bottom:0.5em;"> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Topology</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Random_graph" title="Random graph">Random graph</a></li> <li><a href="/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model" title="Erdős–Rényi model">Erdős–Rényi</a></li> <li><a href="/wiki/Barab%C3%A1si%E2%80%93Albert_model" title="Barabási–Albert model">Barabási–Albert</a></li> <li><a href="/wiki/Bianconi%E2%80%93Barab%C3%A1si_model" title="Bianconi–Barabási model">Bianconi–Barabási</a></li> <li><a href="/wiki/Fitness_model_(network_theory)" title="Fitness model (network theory)">Fitness model</a></li> <li><a href="/wiki/Watts%E2%80%93Strogatz_model" title="Watts–Strogatz model">Watts–Strogatz</a></li> <li><a href="/wiki/Exponential_random_graph_models" class="mw-redirect" title="Exponential random graph models">Exponential random (ERGM)</a></li> <li><a href="/wiki/Random_geometric_graph" title="Random geometric graph">Random geometric (RGG)</a></li> <li><a href="/wiki/Hyperbolic_geometric_graph" title="Hyperbolic geometric graph">Hyperbolic (HGN)</a></li> <li><a href="/wiki/Hierarchical_network_model" title="Hierarchical network model">Hierarchical</a></li> <li><a href="/wiki/Stochastic_block_model" title="Stochastic block model">Stochastic block</a></li> <li><a href="/wiki/Blockmodeling" title="Blockmodeling">Blockmodeling</a></li> <li><a href="/wiki/Maximum-entropy_random_graph_model" title="Maximum-entropy random graph model">Maximum entropy</a></li> <li><a href="/wiki/Soft_configuration_model" title="Soft configuration model">Soft configuration</a></li> <li><a href="/wiki/Lancichinetti%E2%80%93Fortunato%E2%80%93Radicchi_benchmark" title="Lancichinetti–Fortunato–Radicchi benchmark">LFR Benchmark</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Dynamics</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Boolean_network" title="Boolean network">Boolean network</a></li> <li><a href="/wiki/Agent-based_model" title="Agent-based model">agent based</a></li> <li><a href="/wiki/Epidemic_model" class="mw-redirect" title="Epidemic model">Epidemic</a>/<a href="/wiki/SIR_model" class="mw-redirect" title="SIR model">SIR</a></li></ul></td> </tr></tbody></table></td> </tr><tr><th class="sidebar-heading"> <div class="hlist"><ul><li>Lists</li><li>Categories</li></ul></div></th></tr><tr><td class="sidebar-content hlist" style="padding-top:0.2em;padding-bottom:0.5em;"> <ul><li><a href="/wiki/List_of_network_theory_topics" title="List of network theory topics">Topics</a></li> <li><a href="/wiki/Social_network_analysis_software" title="Social network analysis software">Software</a></li> <li><a href="/wiki/List_of_network_scientists" title="List of network scientists">Network scientists</a></li></ul> <ul><li><a href="/wiki/Category:Network_theory" title="Category:Network theory">Category:Network theory</a></li> <li><a href="/wiki/Category:Graph_theory" title="Category:Graph theory">Category:Graph theory</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><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:Network_science" title="Template:Network science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Network_science" title="Template talk:Network science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Network_science" title="Special:EditPage/Template:Network science"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In the context of <a href="/wiki/Network_theory" title="Network theory">network theory</a>, a <b>complex network</b> is a <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">graph</a> (network) with non-trivial <a href="/wiki/Topological" class="mw-redirect" title="Topological">topological</a> features—features that do not occur in simple networks such as <a href="/wiki/Lattice_graph" title="Lattice graph">lattices</a> or <a href="/wiki/Random_graph" title="Random graph">random graphs</a> but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research<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><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> (since 2000) inspired largely by empirical findings of real-world networks such as <a href="/wiki/Computer_network" title="Computer network">computer networks</a>, <a href="/wiki/Biological_network" title="Biological network">biological networks</a>, technological networks, <a href="/wiki/Connectome" title="Connectome">brain networks</a>,<sup id="cite_ref-Bassett_353–364_3-0" class="reference"><a href="#cite_note-Bassett_353–364-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-AlexF_4-0" class="reference"><a href="#cite_note-AlexF-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Climate_networks" class="mw-redirect" title="Climate networks">climate networks</a> and <a href="/wiki/Social_network" title="Social network">social networks</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_network&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Most <a href="/wiki/Social_network" title="Social network">social</a>, <a href="/wiki/Biological_network" title="Biological network">biological</a>, and <a href="/wiki/Computer_network" title="Computer network">technological networks</a> display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the <a href="/wiki/Degree_distribution" title="Degree distribution">degree distribution</a>, a high <a href="/wiki/Clustering_coefficient" title="Clustering coefficient">clustering coefficient</a>, <a href="/wiki/Assortativity" title="Assortativity">assortativity</a> or disassortativity among vertices, <a href="/wiki/Community_structure" title="Community structure">community structure</a>, and <a href="/wiki/Hierarchy" title="Hierarchy">hierarchical structure</a>. In the case of directed networks these features also include <a href="/wiki/Reciprocity_in_network" class="mw-redirect" title="Reciprocity in network">reciprocity</a>, triad significance profile and other features. In contrast, many of the mathematical models of networks that have been studied in the past, such as <a href="/wiki/Lattice_graph" title="Lattice graph">lattices</a> and <a href="/wiki/Random_graph" title="Random graph">random graphs</a>, do not show these features. The most complex structures can be realized by networks with a medium number of interactions.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This corresponds to the fact that the maximum information content (<a href="/wiki/Entropy_(information_theory)" title="Entropy (information theory)">entropy</a>) is obtained for medium probabilities. </p><p>Two well-known and much studied classes of complex networks are <a href="/wiki/Scale-free_networks" class="mw-redirect" title="Scale-free networks">scale-free networks</a><sup id="cite_ref-frst_6-0" class="reference"><a href="#cite_note-frst-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Small-world_networks" class="mw-redirect" title="Small-world networks">small-world networks</a>,<sup id="cite_ref-sec_7-0" class="reference"><a href="#cite_note-sec-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> whose discovery and definition are canonical case-studies in the field. Both are characterized by specific structural features—<a href="/wiki/Power-law" class="mw-redirect" title="Power-law">power-law</a> <a href="/wiki/Degree_distribution" title="Degree distribution">degree distributions</a> for the former and short path lengths and high <a href="/wiki/Clustering_coefficient" title="Clustering coefficient">clustering</a> for the latter. However, as the study of complex networks has continued to grow in importance and popularity, many other aspects of network structures have attracted attention as well. </p><p>The field continues to develop at a brisk pace, and has brought together researchers from many areas including <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, <a href="/wiki/Physics" title="Physics">physics</a>, electric power systems,<sup id="cite_ref-Saleh_1381_9-0" class="reference"><a href="#cite_note-Saleh_1381-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Biology" title="Biology">biology</a>, <a href="/wiki/Climate" title="Climate">climate</a>, <a href="/wiki/Computer_science" title="Computer science">computer science</a>, <a href="/wiki/Sociology" title="Sociology">sociology</a>, <a href="/wiki/Epidemiology" title="Epidemiology">epidemiology</a>, and others.<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> Ideas and tools from network science and engineering have been applied to the analysis of metabolic and genetic regulatory networks; the study of ecosystem stability and robustness;<sup id="cite_ref-johnson2014_11-0" class="reference"><a href="#cite_note-johnson2014-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> clinical science;<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> the modeling and design of scalable communication networks such as the generation and visualization of complex wireless networks;<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> and a broad range of other practical issues. Network science is the topic of many conferences in a variety of different fields, and has been the subject of numerous books both for the lay person and for the expert. </p> <div class="mw-heading mw-heading2"><h2 id="Scale-free_networks">Scale-free networks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_network&action=edit&section=2" title="Edit section: Scale-free networks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Scale-free_networks" class="mw-redirect" title="Scale-free networks">Scale-free networks</a></div> <figure class="mw-default-size" 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>An example of complex scale-free network</figcaption></figure><p>A network is called scale-free<sup id="cite_ref-frst_6-1" class="reference"><a href="#cite_note-frst-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><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>  if its degree distribution, i.e., the probability that a node selected uniformly at random has a certain number of links (degree), follows a mathematical function called a <a href="/wiki/Power_law" title="Power law">power law</a>. The power law implies that the degree distribution of these networks has no characteristic scale. In contrast, networks with a single well-defined scale are somewhat similar to a lattice in that every node has (roughly) the same degree. Examples of networks with a single scale include the <a href="/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model" title="Erdős–Rényi model">Erdős–Rényi (ER) random graph</a>, <a href="/w/index.php?title=Random_regular_graphs&action=edit&redlink=1" class="new" title="Random regular graphs (page does not exist)">random regular graphs</a>, <a href="/w/index.php?title=Regular_lattices&action=edit&redlink=1" class="new" title="Regular lattices (page does not exist)">regular lattices</a>, and <a href="/wiki/Hypercube" title="Hypercube">hypercubes</a>. Some models of growing networks that produce scale-invariant degree distributions are the <a href="/wiki/Barab%C3%A1si%E2%80%93Albert_model" title="Barabási–Albert model">Barabási–Albert model</a> and the <a href="/wiki/Fitness_model_(network_theory)" title="Fitness model (network theory)">fitness model</a>. In a network with a scale-free degree distribution, some vertices have a degree that is orders of magnitude larger than the average - these vertices are often called "hubs", although this language is misleading as, by definition, there is no inherent threshold above which a node can be viewed as a hub. If there were such a threshold, the network would not be scale-free. </p><p>Interest in scale-free networks began in the late 1990s with the reporting of discoveries of power-law degree distributions in real world networks such as the <a href="/wiki/World_Wide_Web" title="World Wide Web">World Wide Web</a>, the network of <a href="/wiki/Autonomous_system_(Internet)" title="Autonomous system (Internet)">Autonomous systems</a> (ASs), some networks of Internet routers, protein interaction networks, email networks, etc. Most of these reported "power laws" fail when challenged with rigorous statistical testing, but the more general idea of heavy-tailed degree distributions—which many of these networks do genuinely exhibit (before finite-size effects occur) -- are very different from what one would expect if edges existed independently and at random (i.e., if they followed a <a href="/wiki/Poisson_distribution" title="Poisson distribution">Poisson distribution</a>). There are many different ways to build a network with a power-law degree distribution. The <a href="/wiki/Yule-Simon_distribution" class="mw-redirect" title="Yule-Simon distribution">Yule process</a> is a canonical generative process for power laws, and has been known since 1925. However, it is known by many other names due to its frequent reinvention, e.g., The Gibrat principle by <a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert A. Simon</a>, the <a href="/wiki/Matthew_effect_(sociology)" class="mw-redirect" title="Matthew effect (sociology)">Matthew effect</a>, cumulative advantage and, <a href="/wiki/Preferential_attachment" title="Preferential attachment">preferential attachment</a> by <a href="/wiki/Albert-L%C3%A1szl%C3%B3_Barab%C3%A1si" title="Albert-László Barabási">Barabási</a> and Albert for power-law degree distributions. Recently, <a href="/wiki/Hyperbolic_Geometric_Graph" class="mw-redirect" title="Hyperbolic Geometric Graph">Hyperbolic Geometric Graphs</a> have been suggested as yet another way of constructing scale-free networks. </p><p>Some networks with a power-law degree distribution (and specific other types of structure) can be highly resistant to the random deletion of vertices—i.e., the vast majority of vertices remain connected together in a giant component. Such networks can also be quite sensitive to targeted attacks aimed at fracturing the network quickly. When the graph is uniformly random except for the degree distribution, these critical vertices are the ones with the highest degree, and have thus been implicated in the spread of disease (natural and artificial) in social and communication networks, and in the spread of fads (both of which are modeled by a <a href="/wiki/Percolation" title="Percolation">percolation</a> or <a href="/wiki/Branching_process" title="Branching process">branching process</a>). While random graphs (ER) have an average distance of order log N<sup id="cite_ref-sec_7-1" class="reference"><a href="#cite_note-sec-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> between nodes, where N is the number of nodes, scale free graph can have a distance of log log N. </p> <div class="mw-heading mw-heading2"><h2 id="Small-world_networks">Small-world networks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_network&action=edit&section=3" title="Edit section: Small-world networks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Small-world_network" title="Small-world network">Small-world network</a></div> <p>A network is called a small-world network<sup id="cite_ref-sec_7-2" class="reference"><a href="#cite_note-sec-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> by analogy with the <a href="/wiki/Small-world_phenomenon" class="mw-redirect" title="Small-world phenomenon">small-world phenomenon</a> (popularly known as <a href="/wiki/Six_degrees_of_separation" title="Six degrees of separation">six degrees of separation</a>). The small world hypothesis, which was first described by the Hungarian writer <a href="/wiki/Frigyes_Karinthy" title="Frigyes Karinthy">Frigyes Karinthy</a> in 1929, and tested experimentally by <a href="/wiki/Stanley_Milgram" title="Stanley Milgram">Stanley Milgram</a> (1967), is the idea that two arbitrary people are connected by only six degrees of separation, i.e. the diameter of the corresponding graph of social connections is not much larger than six. In 1998, <a href="/wiki/Duncan_J._Watts" title="Duncan J. Watts">Duncan J. Watts</a> and <a href="/wiki/Steven_Strogatz" title="Steven Strogatz">Steven Strogatz</a> published the first small-world network model, which through a single parameter smoothly interpolates between a random graph and a lattice.<sup id="cite_ref-sec_7-3" class="reference"><a href="#cite_note-sec-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Their model demonstrated that with the addition of only a small number of long-range links, a regular graph, in which the diameter is proportional to the size of the network, can be transformed into a "small world" in which the average number of edges between any two vertices is very small (mathematically, it should grow as the logarithm of the size of the network), while the clustering coefficient stays large. It is known that a wide variety of abstract graphs exhibit the small-world property, e.g., random graphs and scale-free networks. Further, real world networks such as the <a href="/wiki/World_Wide_Web" title="World Wide Web">World Wide Web</a> and the metabolic network also exhibit this property. </p><p>In the scientific literature on networks, there is some ambiguity associated with the term "small world". In addition to referring to the size of the diameter of the network, it can also refer to the co-occurrence of a small diameter and a high <a href="/wiki/Clustering_coefficient" title="Clustering coefficient">clustering coefficient</a>. The clustering coefficient is a metric that represents the density of triangles in the network. For instance, sparse random graphs have a vanishingly small clustering coefficient while real world networks often have a coefficient significantly larger. Scientists point to this difference as suggesting that edges are correlated in real world networks. Approaches have been developed to generate network models that exhibit high correlations, while preserving the desired degree distribution and small-world properties. These approaches can be used to generate analytically solvable toy models for research into these systems.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Spatial_networks">Spatial networks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_network&action=edit&section=4" title="Edit section: Spatial networks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Spatial_network" title="Spatial network">Spatial network</a></div> <p>Many real networks are embedded in space. Examples include, transportation and other infrastructure networks, brain networks.<sup id="cite_ref-Bassett_353–364_3-1" class="reference"><a href="#cite_note-Bassett_353–364-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-AlexF_4-1" class="reference"><a href="#cite_note-AlexF-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Several models for spatial networks have been developed.<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> </p> <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=Complex_network&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Community_structure" title="Community structure">Community structure</a></li> <li><a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">Complex adaptive system</a></li> <li><a href="/wiki/Complex_systems" class="mw-redirect" title="Complex systems">Complex systems</a></li> <li><a href="/wiki/Dual-phase_evolution" title="Dual-phase evolution">Dual-phase evolution</a></li> <li><a href="/wiki/Dynamic_network_analysis" title="Dynamic network analysis">Dynamic network analysis</a></li> <li><a href="/wiki/Interdependent_networks" title="Interdependent networks">Interdependent networks</a></li> <li><a href="/wiki/Multidimensional_network" title="Multidimensional network">Multidimensional network</a></li> <li><a href="/wiki/Network_theory" title="Network theory">Network theory</a></li> <li><a href="/wiki/Network_science" title="Network science">Network science</a></li> <li><a href="/wiki/Percolation_theory" title="Percolation theory">Percolation theory</a></li> <li><a href="/wiki/Random_graph" title="Random graph">Random graph</a></li> <li><a href="/wiki/Random_graph_theory_of_gelation" title="Random graph theory of gelation">Random graph theory of gelation</a></li> <li><a href="/wiki/Scale-free_networks" class="mw-redirect" title="Scale-free networks">Scale-free networks</a></li> <li><a href="/wiki/Small_world_networks" class="mw-redirect" title="Small world networks">Small world networks</a></li> <li><a href="/wiki/Spatial_network" title="Spatial network">Spatial network</a></li> <li><a href="/wiki/Trophic_coherence" title="Trophic coherence">Trophic coherence</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Books">Books</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_network&action=edit&section=6" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>B. S. Manoj, Abhishek Chakraborty, and Rahul Singh, <i>Complex Networks: A Networking and Signal Processing Perspective</i>, Pearson, New York, USA, February 2018. <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-478699-5" title="Special:BookSources/978-0-13-478699-5">978-0-13-478699-5</a></li> <li>S.N. Dorogovtsev and J.F.F. Mendes, <i>Evolution of Networks: From biological networks to the Internet and WWW</i>, Oxford University Press, 2003, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-851590-1" title="Special:BookSources/0-19-851590-1">0-19-851590-1</a></li> <li>Duncan J. Watts, <i>Six Degrees: The Science of a Connected Age</i>, W. W. Norton & Company, 2003, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-393-04142-5" title="Special:BookSources/0-393-04142-5">0-393-04142-5</a></li> <li>Duncan J. Watts, <i>Small Worlds: The Dynamics of Networks between Order and Randomness</i>, Princeton University Press, 2003, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-11704-7" title="Special:BookSources/0-691-11704-7">0-691-11704-7</a></li> <li>Albert-László Barabási, <i>Linked: How Everything is Connected to Everything Else</i>, 2004, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-452-28439-2" title="Special:BookSources/0-452-28439-2">0-452-28439-2</a></li> <li>Alain Barrat, Marc Barthelemy, Alessandro Vespignani, <i>Dynamical processes on complex networks</i>, Cambridge University Press, 2008, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-87950-7" title="Special:BookSources/978-0-521-87950-7">978-0-521-87950-7</a></li> <li>Stefan Bornholdt (editor) and Heinz Georg Schuster (editor), <i>Handbook of Graphs and Networks: From the Genome to the Internet</i>, 2003, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-527-40336-1" title="Special:BookSources/3-527-40336-1">3-527-40336-1</a></li> <li>Guido Caldarelli, <i>Scale-Free Networks</i>, Oxford University Press, 2007, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-921151-7" title="Special:BookSources/978-0-19-921151-7">978-0-19-921151-7</a></li> <li>Guido Caldarelli, Michele Catanzaro, <i>Networks: A Very Short Introduction</i> Oxford University Press, 2012, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-958807-7" title="Special:BookSources/978-0-19-958807-7">978-0-19-958807-7</a></li> <li>E. Estrada, "The Structure of Complex Networks: Theory and Applications", Oxford University Press, 2011, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-199-59175-6" title="Special:BookSources/978-0-199-59175-6">978-0-199-59175-6</a></li> <li>Mark Newman, <i>Networks: An Introduction</i>, Oxford University Press, 2010, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-920665-0" title="Special:BookSources/978-0-19-920665-0">978-0-19-920665-0</a></li> <li>Mark Newman, Albert-László Barabási, and Duncan J. Watts, <i>The Structure and Dynamics of Networks</i>, Princeton University Press, Princeton, 2006, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11357-9" title="Special:BookSources/978-0-691-11357-9">978-0-691-11357-9</a></li> <li>R. Pastor-Satorras and A. Vespignani, <i>Evolution and Structure of the Internet: A statistical physics approach</i>, Cambridge University Press, 2004, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-82698-5" title="Special:BookSources/0-521-82698-5">0-521-82698-5</a></li> <li>T. Lewis, Network Science, Wiley 2009,</li> <li>Niloy Ganguly (editor), Andreas Deutsch (editor) and Animesh Mukherjee (editor), <i>Dynamics On and Of Complex Networks Applications to Biology, Computer Science, and the Social Sciences</i>, 2009, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8176-4750-6" title="Special:BookSources/978-0-8176-4750-6">978-0-8176-4750-6</a></li> <li>Vito Latora, Vincenzo Nicosia, Giovanni Russo, <i>Complex Networks: Principles, Methods and Applications</i>, Cambridge University Press, 2017, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-10318-4" title="Special:BookSources/978-1-107-10318-4">978-1-107-10318-4</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=Complex_network&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output 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ambox-More_footnotes_needed" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article includes a list of <a href="/wiki/Wikipedia:Citing_sources#General_references" title="Wikipedia:Citing sources">general references</a>, but <b>it lacks sufficient corresponding <a 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