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. (2006) In-degree and pageRank of web pages: Why do they follow similar power laws? [Report]

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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.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/66196
Official URL:http://www.math.utwente.nl/publications/2006/1807.pdf
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