<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>clustering — NetworkX 1.8.1 documentation</title> <link rel="stylesheet" href="../../_static/networkx.css" type="text/css" /> <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" /> <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../../', VERSION: '1.8.1', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: false }; </script> <script type="text/javascript" src="../../_static/jquery.js"></script> <script type="text/javascript" src="../../_static/underscore.js"></script> <script type="text/javascript" src="../../_static/doctools.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within NetworkX 1.8.1 documentation" href="../../_static/opensearch.xml"/> <link rel="top" title="NetworkX 1.8.1 documentation" href="../../index.html" /> <link rel="up" title="Bipartite" href="../algorithms.bipartite.html" /> <link rel="next" title="average_clustering" href="networkx.algorithms.bipartite.cluster.average_clustering.html" /> <link rel="prev" title="spectral_bipartivity" href="networkx.algorithms.bipartite.spectral.spectral_bipartivity.html" /> </head> <body> <div style="color: black;background-color: white; font-size: 3.2em; text-align: left; padding: 15px 10px 10px 15px"> NetworkX </div> <div class="related"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../../genindex.html" title="General Index" accesskey="I">index</a></li> <li class="right" > <a href="../../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="networkx.algorithms.bipartite.cluster.average_clustering.html" title="average_clustering" accesskey="N">next</a> |</li> <li class="right" > <a href="networkx.algorithms.bipartite.spectral.spectral_bipartivity.html" title="spectral_bipartivity" accesskey="P">previous</a> |</li> <li><a href="http://networkx.github.com/">NetworkX Home </a> | </li> <li><a href="http://networkx.github.com/documentation.html">Documentation </a>| </li> <li><a href="http://networkx.github.com/download.html">Download </a> | </li> <li><a href="http://github.com/networkx">Developer (Github)</a></li> <li><a href="../index.html" >Reference</a> »</li> <li><a href="../pdf_reference.html" >Reference</a> »</li> <li><a href="../algorithms.html" >Algorithms</a> »</li> <li><a href="../algorithms.bipartite.html" accesskey="U">Bipartite</a> »</li> </ul> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"> <h4>Previous topic</h4> <p class="topless"><a href="networkx.algorithms.bipartite.spectral.spectral_bipartivity.html" title="previous chapter">spectral_bipartivity</a></p> <h4>Next topic</h4> <p class="topless"><a href="networkx.algorithms.bipartite.cluster.average_clustering.html" title="next chapter">average_clustering</a></p> <div id="searchbox" style="display: none"> <h3>Quick search</h3> <form class="search" action="../../search.html" method="get"> <input type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> <p class="searchtip" style="font-size: 90%"> Enter search terms or a module, class or function name. </p> </div> <script type="text/javascript">$('#searchbox').show(0);</script> </div> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="clustering"> <h1>clustering<a class="headerlink" href="#clustering" title="Permalink to this headline">¶</a></h1> <dl class="function"> <dt id="networkx.algorithms.bipartite.cluster.clustering"> <tt class="descname">clustering</tt><big>(</big><em>G</em>, <em>nodes=None</em>, <em>mode='dot'</em><big>)</big><a class="headerlink" href="#networkx.algorithms.bipartite.cluster.clustering" title="Permalink to this definition">¶</a></dt> <dd><p>Compute a bipartite clustering coefficient for nodes.</p> <p>The bipartie clustering coefficient is a measure of local density of connections defined as <a class="reference internal" href="#r144">[R144]</a>:</p> <div class="math"> <p><span class="math">c_u = \frac{\sum_{v \in N(N(v))} c_{uv} }{|N(N(u))|}</span></p> </div><p>where <span class="math">N(N(u))</span> are the second order neighbors of <span class="math">u</span> in <span class="math">G</span> excluding <span class="math">u</span>, and <span class="math">c_{uv}</span> is the pairwise clustering coefficient between nodes <span class="math">u</span> and <span class="math">v</span>.</p> <p>The mode selects the function for <span class="math">c_{uv}</span> which can be:</p> <p><span class="math">dot</span>:</p> <div class="math"> <p><span class="math">c_{uv}=\frac{|N(u)\cap N(v)|}{|N(u) \cup N(v)|}</span></p> </div><p><span class="math">min</span>:</p> <div class="math"> <p><span class="math">c_{uv}=\frac{|N(u)\cap N(v)|}{min(|N(u)|,|N(v)|)}</span></p> </div><p><span class="math">max</span>:</p> <div class="math"> <p><span class="math">c_{uv}=\frac{|N(u)\cap N(v)|}{max(|N(u)|,|N(v)|)}</span></p> </div><table class="docutils field-list" frame="void" rules="none"> <col class="field-name" /> <col class="field-body" /> <tbody valign="top"> <tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>G</strong> : graph</p> <blockquote> <div><p>A bipartite graph</p> </div></blockquote> <p><strong>nodes</strong> : list or iterable (optional)</p> <blockquote> <div><p>Compute bipartite clustering for these nodes. The default is all nodes in G.</p> </div></blockquote> <p><strong>mode</strong> : string</p> <blockquote> <div><p>The pariwise bipartite clustering method to be used in the computation. It must be “dot”, “max”, or “min”.</p> </div></blockquote> </td> </tr> <tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>clustering</strong> : dictionary</p> <blockquote class="last"> <div><p>A dictionary keyed by node with the clustering coefficient value.</p> </div></blockquote> </td> </tr> </tbody> </table> <div class="admonition-see-also admonition seealso"> <p class="first admonition-title">See also</p> <p class="last"><a class="reference internal" href="networkx.algorithms.bipartite.cluster.robins_alexander_clustering.html#networkx.algorithms.bipartite.cluster.robins_alexander_clustering" title="networkx.algorithms.bipartite.cluster.robins_alexander_clustering"><tt class="xref py py-obj docutils literal"><span class="pre">robins_alexander_clustering</span></tt></a>, <tt class="xref py py-obj docutils literal"><span class="pre">square_clustering</span></tt>, <a class="reference internal" href="networkx.algorithms.bipartite.cluster.average_clustering.html#networkx.algorithms.bipartite.cluster.average_clustering" title="networkx.algorithms.bipartite.cluster.average_clustering"><tt class="xref py py-obj docutils literal"><span class="pre">average_clustering</span></tt></a></p> </div> <p class="rubric">References</p> <table class="docutils citation" frame="void" id="r144" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label">[R144]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id2">2</a>)</em> Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008). Basic notions for the analysis of large two-mode networks. Social Networks 30(1), 31–48.</td></tr> </tbody> </table> <p class="rubric">Examples</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">networkx.algorithms</span> <span class="kn">import</span> <span class="n">bipartite</span> <span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span> <span class="c"># path graphs are bipartite</span> <span class="gp">>>> </span><span class="n">c</span> <span class="o">=</span> <span class="n">bipartite</span><span class="o">.</span><span class="n">clustering</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="go">0.5</span> <span class="gp">>>> </span><span class="n">c</span> <span class="o">=</span> <span class="n">bipartite</span><span class="o">.</span><span class="n">clustering</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">mode</span><span class="o">=</span><span class="s">'min'</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="go">1.0</span> </pre></div> </div> </dd></dl> </div> </div> </div> </div> <div class="clearer"></div> </div> <div class="related"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="networkx.algorithms.bipartite.cluster.average_clustering.html" title="average_clustering" >next</a> |</li> <li class="right" > <a href="networkx.algorithms.bipartite.spectral.spectral_bipartivity.html" title="spectral_bipartivity" >previous</a> |</li> <li><a href="http://networkx.github.com/">NetworkX Home </a> | </li> <li><a href="http://networkx.github.com/documentation.html">Documentation </a>| </li> <li><a href="http://networkx.github.com/download.html">Download </a> | </li> <li><a href="http://github.com/networkx">Developer (Github)</a></li> <li><a href="../index.html" >Reference</a> »</li> <li><a href="../pdf_reference.html" >Reference</a> »</li> <li><a href="../algorithms.html" >Algorithms</a> »</li> <li><a href="../algorithms.bipartite.html" >Bipartite</a> »</li> </ul> </div> <div class="footer"> © Copyright 2013, NetworkX Developers. 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