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In-Degree and PageRank of Web pages: Why do they follow similar power laws?

N. Litvak·W. R. W. Scheinhardt·Y. Volkovich
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Abstract

The PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that the PageRank obeys a `power law' with the same exponent as the In-Degree. This paper presents a novel mathematical model that explains this phenomenon. The relation between the PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of the 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 behavior of the PageRank and the In-Degree differ only by a multiplicative factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.

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N. Litvak, W. R. W. Scheinhardt, Y. Volkovich. 2006-12-04. In-Degree and PageRank of Web pages: Why do they follow similar power laws?. https://arxiv.org/abs/math/0607507

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