In-Degree and PageRank of web pages: why do they follow similar power laws?

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Litvak, N. and Scheinhardt, W.R.W. and Volkovich, Y.V. (2009) In-Degree and PageRank of web pages: why do they follow similar power laws? Internet Mathematics, 4 (2-3). pp. 175-198. ISSN 1542-7951

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Abstract: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 modelled 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 multiple factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.
Item Type:Article
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/67788
Official URL:http://akpeters.metapress.com/content/n4m911p755020286/
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