This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 GRAPH UTILITIES PACKAGE SYMBOL

PageRanks

 PageRanks[g] give the page rank of the graph g as a rule list.
• 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:
This boosts the page rank of the page by adding more feedback links:
Needs["GraphUtilities`"]
This defines a small graph:
This finds the page rank of each node:
 Out[3]=
This boosts the page rank of the page by adding more feedback links:
 Out[4]=
 Options   (1)
This defines a small directed graph; node 4 is a sink:
This calculates the page rank by linking node 4 with all other nodes:
Without removing the sink, the page rank of node 4 is much larger: