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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> |
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| <!-- Copyright (C) 2004-2008 The Trustees of Indiana University. |
| Use, modification and distribution is subject to the Boost Software |
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| <pre class="literal-block"> |
| namespace graph { |
| template<typename Graph, typename RankMap, typename Done> |
| inline void |
| page_rank(const Graph& g, RankMap rank_map, Done done, |
| typename property_traits<RankMap>::value_type damping = 0.85); |
| |
| template<typename Graph, typename RankMap> |
| inline void |
| page_rank(const Graph& 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><<tt class="docutils literal"><span class="pre">boost/graph/distributed/page_rank.hpp</span></tt>></p> |
| <p>also accessible from</p> |
| <p><<tt class="docutils literal"><span class="pre">boost/graph/page_rank.hpp</span></tt>></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&</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<RankMap>::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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