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<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>
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