<!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>networkx.algorithms.hierarchy — 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="networkx" href="../../networkx.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><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" >Module code</a> »</li> <li><a href="../../networkx.html" accesskey="U">networkx</a> »</li> </ul> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"> <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"> <h1>Source code for networkx.algorithms.hierarchy</h1><div class="highlight"><pre> <span class="c"># -*- coding: utf-8 -*-</span> <span class="sd">"""</span> <span class="sd">Flow Hierarchy.</span> <span class="sd">"""</span> <span class="c"># Copyright (C) 2004-2011 by</span> <span class="c"># Aric Hagberg <hagberg@lanl.gov></span> <span class="c"># Dan Schult <dschult@colgate.edu></span> <span class="c"># Pieter Swart <swart@lanl.gov></span> <span class="c"># All rights reserved.</span> <span class="c"># BSD license.</span> <span class="kn">import</span> <span class="nn">networkx</span> <span class="kn">as</span> <span class="nn">nx</span> <span class="n">__authors__</span> <span class="o">=</span> <span class="s">"</span><span class="se">\n</span><span class="s">"</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="s">'Ben Edwards (bedwards@cs.unm.edu)'</span><span class="p">])</span> <span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">'flow_hierarchy'</span><span class="p">]</span> <div class="viewcode-block" id="flow_hierarchy"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.hierarchy.flow_hierarchy.html#networkx.algorithms.hierarchy.flow_hierarchy">[docs]</a><span class="k">def</span> <span class="nf">flow_hierarchy</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span> <span class="sd">"""Returns the flow hierarchy of a directed network.</span> <span class="sd"> Flow hierarchy is defined as the fraction of edges not participating</span> <span class="sd"> in cycles in a directed graph [1]_.</span> <span class="sd"> Parameters</span> <span class="sd"> ----------</span> <span class="sd"> G : DiGraph or MultiDiGraph</span> <span class="sd"> A directed graph</span> <span class="sd"> weight : key,optional (default=None)</span> <span class="sd"> Attribute to use for node weights. If None the weight defaults to 1.</span> <span class="sd"> Returns</span> <span class="sd"> -------</span> <span class="sd"> h : float</span> <span class="sd"> Flow heirarchy value</span> <span class="sd"> Notes</span> <span class="sd"> -----</span> <span class="sd"> The algorithm described in [1]_ computes the flow hierarchy through</span> <span class="sd"> exponentiation of the adjacency matrix. This function implements an</span> <span class="sd"> alternative approach that finds strongly connected components.</span> <span class="sd"> An edge is in a cycle if and only if it is in a strongly connected</span> <span class="sd"> component, which can be found in `O(m)` time using Tarjan's algorithm.</span> <span class="sd"> References</span> <span class="sd"> ----------</span> <span class="sd"> .. [1] Luo, J.; Magee, C.L. (2011),</span> <span class="sd"> Detecting evolving patterns of self-organizing networks by flow</span> <span class="sd"> hierarchy measurement, Complexity, Volume 16 Issue 6 53-61.</span> <span class="sd"> DOI: 10.1002/cplx.20368</span> <span class="sd"> http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf</span> <span class="sd"> """</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">():</span> <span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXError</span><span class="p">(</span><span class="s">"G must be a digraph in flow_heirarchy"</span><span class="p">)</span> <span class="n">scc</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">strongly_connected_components</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="k">return</span> <span class="mf">1.</span><span class="o">-</span><span class="nb">sum</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">weight</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">scc</span><span class="p">)</span><span class="o">/</span><span class="nb">float</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">weight</span><span class="p">))</span></div> </pre></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><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" >Module code</a> »</li> <li><a href="../../networkx.html" >networkx</a> »</li> </ul> </div> <div class="footer"> © Copyright 2013, NetworkX Developers. Last updated on Oct 23, 2013. Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.1.3. </div> </body> </html>