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<div class="section" id="closeness-centrality">
<h1>closeness_centrality<a class="headerlink" href="#closeness-centrality" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="networkx.algorithms.bipartite.centrality.closeness_centrality">
<tt class="descname">closeness_centrality</tt><big>(</big><em>G</em>, <em>nodes</em>, <em>normalized=True</em><big>)</big><a class="reference internal" href="../../_modules/networkx/algorithms/bipartite/centrality.html#closeness_centrality"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#networkx.algorithms.bipartite.centrality.closeness_centrality" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the closeness centrality for nodes in a bipartite network.</p>
<p>The closeness of a node is the distance to all other nodes in the
graph or in the case that the graph is not connected to all other nodes
in the connected component containing that node.</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</strong> : graph</p>
<blockquote>
<div><p>A bipartite network</p>
</div></blockquote>
<p><strong>nodes</strong> : list or container</p>
<blockquote>
<div><p>Container with all nodes in one bipartite node set.</p>
</div></blockquote>
<p><strong>normalized</strong> : bool, optional</p>
<blockquote>
<div><p>If True (default) normalize by connected component size.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>closeness</strong> : dictionary</p>
<blockquote class="last">
<div><p>Dictionary keyed by node with bipartite closeness centrality
as the value.</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"><a class="reference internal" href="networkx.algorithms.bipartite.centrality.betweenness_centrality.html#networkx.algorithms.bipartite.centrality.betweenness_centrality" title="networkx.algorithms.bipartite.centrality.betweenness_centrality"><tt class="xref py py-obj docutils literal"><span class="pre">betweenness_centrality</span></tt></a>, <a class="reference internal" href="networkx.algorithms.bipartite.centrality.degree_centrality.html#networkx.algorithms.bipartite.centrality.degree_centrality" title="networkx.algorithms.bipartite.centrality.degree_centrality"><tt class="xref py py-obj docutils literal"><span class="pre">degree_centrality</span></tt></a>, <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>, <tt class="xref py py-obj docutils literal"><span class="pre">is_bipartite</span></tt></p>
</div>
<p class="rubric">Notes</p>
<p>The nodes input parameter must conatin all nodes in one bipartite node set,
but the dictionary returned contains all nodes from both node sets.</p>
<p>Closeness centrality is normalized by the minimum distance possible.
In the bipartite case the minimum distance for a node in one bipartite
node set is 1 from all nodes in the other node set and 2 from all
other nodes in its own set <a class="reference internal" href="#r141">[R141]</a>. Thus the closeness centrality
for node <span class="math">v</span> in the two bipartite sets <span class="math">U</span> with
<span class="math">n</span> nodes and <span class="math">V</span> with <span class="math">m</span> nodes is</p>
<div class="math">
<p><span class="math">c_{v} = \frac{m + 2(n - 1)}{d}, \mbox{for} v \in U,
c_{v} = \frac{n + 2(m - 1)}{d}, \mbox{for} v \in V,</span></p>
</div><p>where <span class="math">d</span> is the sum of the distances from <span class="math">v</span> to all
other nodes.</p>
<p>Higher values of closeness indicate higher centrality.</p>
<p>As in the unipartite case, setting normalized=True causes the
values to normalized further to n-1 / size(G)-1 where n is the
number of nodes in the connected part of graph containing the
node. If the graph is not completely connected, this algorithm
computes the closeness centrality for each connected part
separately.</p>
<p class="rubric">References</p>
<table class="docutils citation" frame="void" id="r141" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[R141]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id2">2</a>)</em> Borgatti, S.P. and Halgin, D. In press. “Analyzing Affiliation
Networks”. In Carrington, P. and Scott, J. (eds) The Sage Handbook
of Social Network Analysis. Sage Publications.
<a class="reference external" href="http://www.steveborgatti.com/papers/bhaffiliations.pdf">http://www.steveborgatti.com/papers/bhaffiliations.pdf</a></td></tr>
</tbody>
</table>
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