@book{93a9e55707d2410990d0a526acf96eec,

title = "In-degree and pageRank of web pages: Why do they follow similar power laws?",

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/l 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.",

keywords = "IR-66196, METIS-238082, MSC-40E05, MSC-90B15, MSC-68P10, EWI-6125",

author = "Nelli Litvak and Scheinhardt, {Willem R.W.} and Y. Volkovich",

note = "eemcs-eprint-6125 ",

year = "2006",

month = may,

language = "Undefined",

series = "Applied Mathematics Memoranda",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1807",

}