Determining factors behind the PageRank log-log plot
arXiv:0704.2694 · doi:10.1007/978-3-540-77004-6_9
Abstract
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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