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<h1 class="title"><a class="reference external" href="http://www.osl.iu.edu/research/pbgl"><img align="middle" alt="Parallel BGL" class="align-middle" src="pbgl-logo.png" /></a> PageRank</h1>

<!-- Copyright (C) 2004-2008 The Trustees of Indiana University.
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<pre class="literal-block">
namespace graph {
  template&lt;typename Graph, typename RankMap, typename Done&gt;
  inline void
  page_rank(const Graph&amp; g, RankMap rank_map, Done done,
            typename property_traits&lt;RankMap&gt;::value_type damping = 0.85);

  template&lt;typename Graph, typename RankMap&gt;
  inline void
  page_rank(const Graph&amp; g, RankMap rank_map);
}
</pre>
<p>The <tt class="docutils literal"><span class="pre">page_rank</span></tt> algorithm computes the ranking of vertices in a
graph, based on the connectivity of a directed graph <a class="citation-reference" href="#pbmw98" id="id1">[PBMW98]</a>. The
idea of PageRank is based on a random model of a Web surfer, who
starts a random web page and then either follows a link from that web
page (choosing from the links randomly) or jumps to a completely
different web page (not necessarily linked from the current
page). The PageRank of each page is the probability of the random web
surfer visiting that page.</p>
<div class="contents topic" id="contents">
<p class="topic-title first">Contents</p>
<ul class="simple">
<li><a class="reference internal" href="#where-defined" id="id2">Where Defined</a></li>
<li><a class="reference internal" href="#parameters" id="id3">Parameters</a></li>
<li><a class="reference internal" href="#complexity" id="id4">Complexity</a><ul>
<li><a class="reference internal" href="#bibliography" id="id5">Bibliography</a></li>
</ul>
</li>
</ul>
</div>
<div class="section" id="where-defined">
<h1><a class="toc-backref" href="#id2">Where Defined</a></h1>
<p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/page_rank.hpp</span></tt>&gt;</p>
<p>also accessible from</p>
<p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/page_rank.hpp</span></tt>&gt;</p>
</div>
<div class="section" id="parameters">
<h1><a class="toc-backref" href="#id3">Parameters</a></h1>
<dl class="docutils">
<dt>IN: <tt class="docutils literal"><span class="pre">Graph&amp;</span> <span class="pre">g</span></tt></dt>
<dd>The graph type must be a model of <a class="reference external" href="DistributedVertexListGraph.html">Distributed Vertex List Graph</a> and
<a class="reference external" href="DistributedEdgeListGraph.html">Distributed Edge List Graph</a>. The graph must be directed.</dd>
<dt>OUT: <tt class="docutils literal"><span class="pre">RankMap</span> <span class="pre">rank</span></tt></dt>
<dd>Stores the rank of each vertex. The type <tt class="docutils literal"><span class="pre">RankMap</span></tt> must model the
<a class="reference external" href="http://www.boost.org/libs/property_map/ReadWritePropertyMap.html">Read/Write Property Map</a> concept and must be a <a class="reference external" href="distributed_property_map.html">distributed
property map</a>. Its key type must be the vertex descriptor of the
graph type and its value type must be a floating-point or rational
type.</dd>
<dt>IN: <tt class="docutils literal"><span class="pre">Done</span> <span class="pre">done</span></tt></dt>
<dd><p class="first">A function object that determines when the PageRank algorithm
should complete. It will be passed two parameters, the rank map and
a reference to the graph, and should return <tt class="docutils literal"><span class="pre">true</span></tt> when the
algorithm should terminate.</p>
<p class="last"><strong>Default</strong>: <tt class="docutils literal"><span class="pre">graph::n_iterations(20)</span></tt></p>
</dd>
<dt>IN: <tt class="docutils literal"><span class="pre">typename</span> <span class="pre">property_traits&lt;RankMap&gt;::value_type</span> <span class="pre">damping</span></tt></dt>
<dd><p class="first">The damping factor is the probability that the Web surfer will
select an outgoing link from the current page instead of jumping to
a random page.</p>
<p class="last"><strong>Default</strong>: 0.85</p>
</dd>
</dl>
</div>
<div class="section" id="complexity">
<h1><a class="toc-backref" href="#id4">Complexity</a></h1>
<p>Each iteration of PageRank requires <em>O((V + E)/p)</em> time on <em>p</em>
processors and performs <em>O(V)</em> communication. The number of
iterations is dependent on the input to the algorithm.</p>
<div class="section" id="bibliography">
<h2><a class="toc-backref" href="#id5">Bibliography</a></h2>
<table class="docutils citation" frame="void" id="pbmw98" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[PBMW98]</a></td><td>Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry
Winograd. The PageRank Citation Ranking: Bringing Order to the
Web. Technical report, Stanford Digital Library Technologies Project,
November 1998.</td></tr>
</tbody>
</table>
<hr class="docutils" />
<p>Copyright (C) 2005 The Trustees of Indiana University.</p>
<p>Authors: Douglas Gregor and Andrew Lumsdaine</p>
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