Internet Mathematics

In-Degree and PageRank: Why Do They Follow Similar Power Laws?

N. Litvak, W. R. W. Scheinhardt, and Y. Volkovich

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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 prove analytically 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.

Article information

Internet Math., Volume 4, Number 2-3 (2007), 175-198.

First available in Project Euclid: 27 May 2009

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Litvak, N.; Scheinhardt, W. R. W.; Volkovich, Y. In-Degree and PageRank: Why Do They Follow Similar Power Laws?. Internet Math. 4 (2007), no. 2-3, 175--198.

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