In-Degree and PageRank of Web pages: Why do they follow similar power laws?
<|reference_start|>In-Degree and PageRank of Web pages: Why do they follow similar power laws?: 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.<|reference_end|>
@article{litvak2006in-degree,
    title={In-Degree and PageRank of Web pages: Why do they follow similar power
  laws?},
    author={N. Litvak, W.R.W. Scheinhardt and Y. Volkovich},
    journal={arXiv preprint arXiv:math/0607507},
    year={2006},
    number={Memorandum 1807, Dept. of Applied. Mathematics, University of Twente},
    archivePrefix={arXiv},
    eprint={math/0607507},
    primaryClass={math.PR cs.IR}
}