<!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>projected_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="Bipartite" href="../algorithms.bipartite.html" /> <link rel="next" title="weighted_projected_graph" href="networkx.algorithms.bipartite.projection.weighted_projected_graph.html" /> <link rel="prev" title="biadjacency_matrix" href="networkx.algorithms.bipartite.basic.biadjacency_matrix.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.bipartite.projection.weighted_projected_graph.html" title="weighted_projected_graph" accesskey="N">next</a> |</li> <li class="right" > <a href="networkx.algorithms.bipartite.basic.biadjacency_matrix.html" title="biadjacency_matrix" 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.bipartite.html" accesskey="U">Bipartite</a> »</li> </ul> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"> <h4>Previous topic</h4> <p class="topless"><a href="networkx.algorithms.bipartite.basic.biadjacency_matrix.html" title="previous chapter">biadjacency_matrix</a></p> <h4>Next topic</h4> <p class="topless"><a href="networkx.algorithms.bipartite.projection.weighted_projected_graph.html" title="next chapter">weighted_projected_graph</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="projected-graph"> <h1>projected_graph<a class="headerlink" href="#projected-graph" title="Permalink to this headline">¶</a></h1> <dl class="function"> <dt id="networkx.algorithms.bipartite.projection.projected_graph"> <tt class="descname">projected_graph</tt><big>(</big><em>B</em>, <em>nodes</em>, <em>multigraph=False</em><big>)</big><a class="reference internal" href="../../_modules/networkx/algorithms/bipartite/projection.html#projected_graph"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#networkx.algorithms.bipartite.projection.projected_graph" title="Permalink to this definition">¶</a></dt> <dd><p>Returns the projection of B onto one of its node sets.</p> <p>Returns the graph G that is the projection of the bipartite graph B onto the specified nodes. They retain their attributes and are connected in G if they have a common neighbor in B.</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>B</strong> : NetworkX graph</p> <blockquote> <div><p>The input graph should be bipartite.</p> </div></blockquote> <p><strong>nodes</strong> : list or iterable</p> <blockquote> <div><p>Nodes to project onto (the “bottom” nodes).</p> </div></blockquote> <p><strong>multigraph: bool (default=False)</strong> :</p> <blockquote> <div><p>If True return a multigraph where the multiple edges represent multiple shared neighbors. They edge key in the multigraph is assigned to the label of the neighbor.</p> </div></blockquote> </td> </tr> <tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>Graph</strong> : NetworkX graph or multigraph</p> <blockquote class="last"> <div><p>A graph that is the projection onto the given nodes.</p> </div></blockquote> </td> </tr> </tbody> </table> <div class="admonition-see-also admonition seealso"> <p class="first admonition-title">See also</p> <p class="last"><tt class="xref py py-obj docutils literal"><span class="pre">is_bipartite</span></tt>, <tt class="xref py py-obj docutils literal"><span class="pre">is_bipartite_node_set</span></tt>, <a class="reference external" href="http://docs.python.org/library/sets.html#sets" title="(in Python v2.7)"><tt class="xref py py-obj docutils literal"><span class="pre">sets</span></tt></a>, <a class="reference internal" href="networkx.algorithms.bipartite.projection.weighted_projected_graph.html#networkx.algorithms.bipartite.projection.weighted_projected_graph" title="networkx.algorithms.bipartite.projection.weighted_projected_graph"><tt class="xref py py-obj docutils literal"><span class="pre">weighted_projected_graph</span></tt></a>, <a class="reference internal" href="networkx.algorithms.bipartite.projection.collaboration_weighted_projected_graph.html#networkx.algorithms.bipartite.projection.collaboration_weighted_projected_graph" title="networkx.algorithms.bipartite.projection.collaboration_weighted_projected_graph"><tt class="xref py py-obj docutils literal"><span class="pre">collaboration_weighted_projected_graph</span></tt></a>, <a class="reference internal" href="networkx.algorithms.bipartite.projection.overlap_weighted_projected_graph.html#networkx.algorithms.bipartite.projection.overlap_weighted_projected_graph" title="networkx.algorithms.bipartite.projection.overlap_weighted_projected_graph"><tt class="xref py py-obj docutils literal"><span class="pre">overlap_weighted_projected_graph</span></tt></a>, <a class="reference internal" href="networkx.algorithms.bipartite.projection.generic_weighted_projected_graph.html#networkx.algorithms.bipartite.projection.generic_weighted_projected_graph" title="networkx.algorithms.bipartite.projection.generic_weighted_projected_graph"><tt class="xref py py-obj docutils literal"><span class="pre">generic_weighted_projected_graph</span></tt></a></p> </div> <p class="rubric">Notes</p> <p>No attempt is made to verify that the input graph B is bipartite. Returns a simple graph that is the projection of the bipartite graph B onto the set of nodes given in list nodes. If multigraph=True then a multigraph is returned with an edge for every shared neighbor.</p> <p>Directed graphs are allowed as input. The output will also then be a directed graph with edges if there is a directed path between the nodes.</p> <p>The graph and node properties are (shallow) copied to the projected graph.</p> <p class="rubric">Examples</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">networkx.algorithms</span> <span class="kn">import</span> <span class="n">bipartite</span> <span class="gp">>>> </span><span class="n">B</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">4</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">bipartite</span><span class="o">.</span><span class="n">projected_graph</span><span class="p">(</span><span class="n">B</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span> <span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">())</span> <span class="go">[1, 3]</span> <span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">())</span> <span class="go">[(1, 3)]</span> </pre></div> </div> <p>If nodes <span class="math">a</span>, and <span class="math">b</span> are connected through both nodes 1 and 2 then building a multigraph results in two edges in the projection onto [<span class="math">a</span>,`b`]:</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">B</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">()</span> <span class="gp">>>> </span><span class="n">B</span><span class="o">.</span><span class="n">add_edges_from</span><span class="p">([(</span><span class="s">'a'</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s">'b'</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s">'a'</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="s">'b'</span><span class="p">,</span> <span class="mi">2</span><span class="p">)])</span> <span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">bipartite</span><span class="o">.</span><span class="n">projected_graph</span><span class="p">(</span><span class="n">B</span><span class="p">,</span> <span class="p">[</span><span class="s">'a'</span><span class="p">,</span> <span class="s">'b'</span><span class="p">],</span> <span class="n">multigraph</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span> <span class="gp">>>> </span><span class="k">print</span><span class="p">([</span><span class="nb">sorted</span><span class="p">((</span><span class="n">u</span><span class="p">,</span><span class="n">v</span><span class="p">))</span> <span class="k">for</span> <span class="n">u</span><span class="p">,</span><span class="n">v</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">edges</span><span class="p">()])</span> <span class="go">[['a', 'b'], ['a', 'b']]</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.algorithms.bipartite.projection.weighted_projected_graph.html" title="weighted_projected_graph" >next</a> |</li> <li class="right" > <a href="networkx.algorithms.bipartite.basic.biadjacency_matrix.html" title="biadjacency_matrix" >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.bipartite.html" >Bipartite</a> »</li> </ul> </div> <div class="footer"> © Copyright 2013, NetworkX Developers. 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