In-degree and PageRank: Why do they follow similar power laws
| Citations: | 3 - 3 self |
BibTeX
@MISC{Litvak_in-degreeand,
author = {N. Litvak and W. R. W. Scheinhardt and Y. Volkovich},
title = {In-degree and PageRank: Why do they follow similar power laws},
year = {}
}
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Abstract
PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is modeled through a stochastic equation, which is inspired by the original definition of PageRank, and is analogous to the well-known distributional identity for the busy period in the M/G/1 queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail distributions of PageRank and In-Degree differ only by a multiplicative constant, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.
