Determining factors behind the PageRank log-log plot

Details Determining factors behind the PageRank log-log plot Determining factors behind the PageRank log-log plot

2007-04-20

arxiv.org/abs/0704.2694v1

LNCS, Algorithms and Models for the Web-Graph,5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007.

Mathematics

Probability

Scientific paper

10.1007/978-3-540-77004-6_9

We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiple coefficient, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Our theoretical predictions show a good agreement with experimental data on three different samples of the Web.

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