PageRanks

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

PageRanks[g]

give the page rank of the graph g as a rule list.

Details and Options

PageRanks functionality is now available in the built-in Wolfram Language function PageRankCentrality.
To use PageRanks, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
The following options can be given:

Tolerance	Automatic	tolerance used for convergence check
TeleportProbability	0.15	probability of visiting random nodes
RemoveSinks	True	whether to remove sinks by linking them with every node

The page rank of a node measures the probability of a web surfer visiting that node. At any node, the surfer is assumed to follow all outlinks with equal probability; in addition, the surfer may visit any node randomly with a certain probability (TeleportProbability).
The page rank algorithm uses an iterative procedure to find the page ranks. When the average change in the page ranks is less than the setting for Tolerance, the iterative process terminates.

This defines a small graph:

This finds the page rank of each node:

PageRanks has been superseded by PageRankCentrality:

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