<!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>average_shortest_path_length — 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="Shortest Paths" href="../algorithms.shortest_paths.html" /> <link rel="next" title="has_path" href="networkx.algorithms.shortest_paths.generic.has_path.html" /> <link rel="prev" title="shortest_path_length" href="networkx.algorithms.shortest_paths.generic.shortest_path_length.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.shortest_paths.generic.has_path.html" title="has_path" accesskey="N">next</a> |</li> <li class="right" > <a href="networkx.algorithms.shortest_paths.generic.shortest_path_length.html" title="shortest_path_length" 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.shortest_paths.html" accesskey="U">Shortest Paths</a> »</li> </ul> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"> <h4>Previous topic</h4> <p class="topless"><a href="networkx.algorithms.shortest_paths.generic.shortest_path_length.html" title="previous chapter">shortest_path_length</a></p> <h4>Next topic</h4> <p class="topless"><a href="networkx.algorithms.shortest_paths.generic.has_path.html" title="next chapter">has_path</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="average-shortest-path-length"> <h1>average_shortest_path_length<a class="headerlink" href="#average-shortest-path-length" title="Permalink to this headline">¶</a></h1> <dl class="function"> <dt id="networkx.algorithms.shortest_paths.generic.average_shortest_path_length"> <tt class="descname">average_shortest_path_length</tt><big>(</big><em>G</em>, <em>weight=None</em><big>)</big><a class="reference internal" href="../../_modules/networkx/algorithms/shortest_paths/generic.html#average_shortest_path_length"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#networkx.algorithms.shortest_paths.generic.average_shortest_path_length" title="Permalink to this definition">¶</a></dt> <dd><p>Return the average shortest path length.</p> <p>The average shortest path length is</p> <div class="math"> <p><span class="math">a =\sum_{s,t \in V} \frac{d(s, t)}{n(n-1)}</span></p> </div><p>where <span class="math">V</span> is the set of nodes in <span class="math">G</span>, <span class="math">d(s, t)</span> is the shortest path from <span class="math">s</span> to <span class="math">t</span>, and <span class="math">n</span> is the number of nodes in <span class="math">G</span>.</p> <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> : NetworkX graph</p> <p><strong>weight</strong> : None or string, optional (default = None)</p> <blockquote> <div><p>If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1.</p> </div></blockquote> </td> </tr> <tr class="field-even field"><th class="field-name">Raises :</th><td class="field-body"><p class="first"><strong>NetworkXError:</strong> :</p> <blockquote class="last"> <div><p>if the graph is not connected.</p> </div></blockquote> </td> </tr> </tbody> </table> <p class="rubric">Examples</p> <div class="highlight-python"><div class="highlight"><pre><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">5</span><span class="p">)</span> <span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">average_shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">))</span> <span class="go">2.0</span> </pre></div> </div> <p>For disconnected graphs you can compute the average shortest path length for each component: >>> G=nx.Graph([(1,2),(3,4)]) >>> for g in nx.connected_component_subgraphs(G): ... print(nx.average_shortest_path_length(g)) 1.0 1.0</p> </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.shortest_paths.generic.has_path.html" title="has_path" >next</a> |</li> <li class="right" > <a href="networkx.algorithms.shortest_paths.generic.shortest_path_length.html" title="shortest_path_length" >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.shortest_paths.html" >Shortest Paths</a> »</li> </ul> </div> <div class="footer"> © Copyright 2013, NetworkX Developers. 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