<!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>expected_degree_graph — 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="Graph generators" href="../generators.html" /> <link rel="next" title="havel_hakimi_graph" href="networkx.generators.degree_seq.havel_hakimi_graph.html" /> <link rel="prev" title="directed_configuration_model" href="networkx.generators.degree_seq.directed_configuration_model.html" /> </head> <body> <div style="color: black;background-color: white; 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Set selfloops=False to produce a graph without self loops.</p> <p>For finite graphs this model doesn’t produce exactly the given expected degree sequence. Instead the expected degrees are as follows.</p> <p>For the case without self loops (selfloops=False),</p> <div class="math"> <p><span class="math">E[deg(u)] = \sum_{v \ne u} p_{uv} = w_u \left( 1 - \frac{w_u}{\sum_k w_k} \right) .</span></p> </div><p>NetworkX uses the standard convention that a self-loop edge counts 2 in the degree of a node, so with self loops (selfloops=True),</p> <div class="math"> <p><span class="math">E[deg(u)] = \sum_{v \ne u} p_{uv} + 2 p_{uu} = w_u \left( 1 + \frac{w_u}{\sum_k w_k} \right) .</span></p> </div><p class="rubric">References</p> <table class="docutils citation" frame="void" id="r254" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label">[R254]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id2">2</a>)</em> Fan Chung and L. Lu, Connected components in random graphs with given expected degree sequences, Ann. Combinatorics, 6, pp. 125-145, 2002.</td></tr> </tbody> </table> <table class="docutils citation" frame="void" id="r255" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label"><a class="fn-backref" href="#id3">[R255]</a></td><td>Joel Miller and Aric Hagberg, Efficient generation of networks with given expected degrees, in Algorithms and Models for the Web-Graph (WAW 2011), Alan Frieze, Paul Horn, and Paweł Prałat (Eds), LNCS 6732, pp. 115-126, 2011.</td></tr> </tbody> </table> <p class="rubric">Examples</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">z</span><span class="o">=</span><span class="p">[</span><span class="mi">10</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">)]</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">expected_degree_graph</span><span class="p">(</span><span class="n">z</span><span class="p">)</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.generators.degree_seq.havel_hakimi_graph.html" title="havel_hakimi_graph" >next</a> |</li> <li class="right" > <a href="networkx.generators.degree_seq.directed_configuration_model.html" title="directed_configuration_model" >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="../generators.html" >Graph generators</a> »</li> </ul> </div> <div class="footer"> © Copyright 2013, NetworkX Developers. 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