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 – ...

• Type: Journal
• Year: 2007
• Where: IM
• Authors: Nelly Litvak, Werner R. W. Scheinhardt, Yana Volkovich
• Keywords: Computer Networks, IM 2007, PageRank, Power Law, Stochastic Equation