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<h1>Source code for networkx.algorithms.approximation.matching</h1><div class="highlight"><pre>
<span class="c"># -*- coding: utf-8 -*-</span>
<span class="sd">"""</span>
<span class="sd">**************</span>
<span class="sd">Graph Matching</span>
<span class="sd">**************</span>
<span class="sd">Given a graph G = (V,E), a matching M in G is a set of pairwise non-adjacent</span>
<span class="sd">edges; that is, no two edges share a common vertex.</span>
<span class="sd">http://en.wikipedia.org/wiki/Matching_(graph_theory)</span>
<span class="sd">"""</span>
<span class="c"># Copyright (C) 2011-2012 by</span>
<span class="c"># Nicholas Mancuso <nick.mancuso@gmail.com></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">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">"min_maximal_matching"</span><span class="p">]</span>
<span class="n">__author__</span> <span class="o">=</span> <span class="s">"""Nicholas Mancuso (nick.mancuso@gmail.com)"""</span>
<div class="viewcode-block" id="min_maximal_matching"><a class="viewcode-back" href="../../../../reference/generated/networkx.algorithms.approximation.matching.min_maximal_matching.html#networkx.algorithms.approximation.matching.min_maximal_matching">[docs]</a><span class="k">def</span> <span class="nf">min_maximal_matching</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">r"""Returns the minimum maximal matching of G. That is, out of all maximal</span>
<span class="sd"> matchings of the graph G, the smallest is returned.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> Undirected graph</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> min_maximal_matching : set</span>
<span class="sd"> Returns a set of edges such that no two edges share a common endpoint</span>
<span class="sd"> and every edge not in the set shares some common endpoint in the set.</span>
<span class="sd"> Cardinality will be 2*OPT in the worst case.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The algorithm computes an approximate solution fo the minimum maximal</span>
<span class="sd"> cardinality matching problem. The solution is no more than 2 * OPT in size.</span>
<span class="sd"> Runtime is `O(|E|)`.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Vazirani, Vijay Approximation Algorithms (2001)</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">nx</span><span class="o">.</span><span class="n">maximal_matching</span><span class="p">(</span><span class="n">G</span><span class="p">)</span></div>
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