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); }

The `page_rank` algorithm computes the ranking of vertices in a
graph, based on the connectivity of a directed graph [PBMW98]. 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.

Contents

<`boost/graph/distributed/page_rank.hpp`>

also accessible from

<`boost/graph/page_rank.hpp`>

- IN:
`Graph& g` - The graph type must be a model of Distributed Vertex List Graph and Distributed Edge List Graph. The graph must be directed.
- OUT:
`RankMap rank` - Stores the rank of each vertex. The type
`RankMap`must model the Read/Write Property Map concept and must be a distributed property map. Its key type must be the vertex descriptor of the graph type and its value type must be a floating-point or rational type. - IN:
`Done done` 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

`true`when the algorithm should terminate.**Default**:`graph::n_iterations(20)`- IN:
`typename property_traits<RankMap>::value_type damping` 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.

**Default**: 0.85

Each iteration of PageRank requires *O((V + E)/p)* time on *p*
processors and performs *O(V)* communication. The number of
iterations is dependent on the input to the algorithm.

[PBMW98] | 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. |

Copyright (C) 2005 The Trustees of Indiana University.

Authors: Douglas Gregor and Andrew Lumsdaine