1. In-Degree and PageRank of Web pages: Why do they follow similar power laws?
- Author
-
Litvak, N., Scheinhardt, W. R. W., and Volkovich, Y.
- Subjects
Mathematics - Probability ,Computer Science - Information Retrieval ,90B15, 68P10, 40E05 - 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/1 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., Comment: 20 pages, 3 figures; typos added; reference added
- Published
- 2006