Random Walks on Directed Networks: the Case of PageRank

Details Random Walks on Directed Networks: the Case of PageRank Random Walks on Directed Networks: the Case of PageRank

2006-04-25

arxiv.org/abs/physics/0604203v2

Physics

Physics and Society

15 pages, 10 figures. Minor modifications, references added, final version to appear in the Special Issue "Complex Networks' S

Scientific paper

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability of being visited. We give some exact results on the distribution of PageRank in the cases in which the damping factor q approaches the two limit values 0 and 1. When q -> 0 and for several classes of graphs the distribution is a power law with exponent 2, regardless of the in-degree distribution. When q -> 1 it can always be derived from the in-degree distribution of the underlying graph, if the out-degree is the same for all nodes.

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