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href="networkx.algorithms.centrality.communicability_centrality.html" title="next chapter">communicability_centrality</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="communicability-exp"> <h1>communicability_exp<a class="headerlink" href="#communicability-exp" title="Permalink to this headline">¶</a></h1> <dl class="function"> <dt id="networkx.algorithms.centrality.communicability_exp"> <tt class="descname">communicability_exp</tt><big>(</big><em>G</em><big>)</big><a class="headerlink" href="#networkx.algorithms.centrality.communicability_exp" title="Permalink to this definition">¶</a></dt> <dd><p>Return communicability between all pairs of nodes in G.</p> <p>Communicability between pair of node (u,v) of node in G is the sum of closed walks of different lengths starting at node u and ending at node v.</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: graph</strong> :</p> </td> </tr> <tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>comm: dictionary of dictionaries</strong> :</p> <blockquote> <div><p>Dictionary of dictionaries keyed by nodes with communicability as the value.</p> </div></blockquote> </td> </tr> <tr class="field-odd 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 undirected and simple.</p> </div></blockquote> </td> </tr> </tbody> </table> <div class="admonition-see-also admonition seealso"> <p class="first admonition-title">See also</p> <dl class="last docutils"> <dt><a class="reference internal" href="networkx.algorithms.centrality.communicability_centrality_exp.html#networkx.algorithms.centrality.communicability_centrality_exp" title="networkx.algorithms.centrality.communicability_centrality_exp"><tt class="xref py py-obj docutils literal"><span class="pre">communicability_centrality_exp</span></tt></a></dt> <dd>Communicability centrality for each node of G using matrix exponential.</dd> <dt><a class="reference internal" href="networkx.algorithms.centrality.communicability_centrality.html#networkx.algorithms.centrality.communicability_centrality" title="networkx.algorithms.centrality.communicability_centrality"><tt class="xref py py-obj docutils literal"><span class="pre">communicability_centrality</span></tt></a></dt> <dd>Communicability centrality for each node in G using spectral decomposition.</dd> <dt><a class="reference internal" href="#networkx.algorithms.centrality.communicability_exp" title="networkx.algorithms.centrality.communicability_exp"><tt class="xref py py-obj docutils literal"><span class="pre">communicability_exp</span></tt></a></dt> <dd>Communicability between all pairs of nodes in G using spectral decomposition.</dd> </dl> </div> <p class="rubric">Notes</p> <p>This algorithm uses matrix exponentiation of the adjacency matrix.</p> <p>Let G=(V,E) be a simple undirected graph. Using the connection between the powers of the adjacency matrix and the number of walks in the graph, the communicability between nodes u and v is <a class="reference internal" href="#r165">[R165]</a>,</p> <div class="math"> <p><span class="math">C(u,v) = (e^A)_{uv},</span></p> </div><p>where <span class="math">A</span> is the adjacency matrix of G.</p> <p class="rubric">References</p> <table class="docutils citation" frame="void" id="r165" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label">[R165]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id2">2</a>)</em> Ernesto Estrada, Naomichi Hatano, “Communicability in complex networks”, Phys. Rev. E 77, 036111 (2008). <a class="reference external" href="http://arxiv.org/abs/0707.0756">http://arxiv.org/abs/0707.0756</a></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">Graph</span><span class="p">([(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">5</span><span class="p">),(</span><span class="mi">5</span><span class="p">,</span><span class="mi">4</span><span class="p">),(</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">),(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">),(</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">),(</span><span class="mi">3</span><span class="p">,</span><span class="mi">6</span><span class="p">)])</span> <span class="gp">>>> </span><span class="n">c</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">communicability_exp</span><span class="p">(</span><span class="n">G</span><span class="p">)</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.centrality.communicability_centrality.html" title="communicability_centrality" >next</a> |</li> <li class="right" > <a href="networkx.algorithms.centrality.communicability.html" title="communicability" >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.centrality.html" >Centrality</a> »</li> </ul> </div> <div class="footer"> © Copyright 2013, NetworkX Developers. 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