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2007

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

13 years 9 months ago
In-Degree and PageRank: Why Do They Follow Similar Power Laws?
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. Categories and Subject Descriptors H.3.3:[Information Storage and Retrieval]: Information Search and Retrieval– Retrieval models; G.3:[Mathematics of Computing]: Probability and statistics – ...
Nelly Litvak, Werner R. W. Scheinhardt, Yana Volko
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2007
Where IM
Authors Nelly Litvak, Werner R. W. Scheinhardt, Yana Volkovich
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