PageRank as a function of the damping factor

PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor that spreads uniformly part of the rank. The choice of is eminently empirical, and in most cases the original suggestion = 0.85 by Brin and Page is still used. Recently, however, the behaviour of PageRank with respect to changes in was discovered to be useful in link-spam detection [21]. Moreover, an analytical justification of the value chosen for is still missing. In this paper, we give the first mathematical analysis of PageRank when changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of close to 1 do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and an extension of the Power Method that approximates them with convergence O tkt for the k-th derivative. Finally, we show a tight connection between iterated c...

• Type: Conference
• Year: 2005
• Where: WWW
• Authors: Paolo Boldi, Massimo Santini, Sebastiano Vigna
• Keywords: Internet Technology, Keywords Web Graph, PageRank Derivatives, PageRank Value, WWW 2005