Mathematical Properties and Analysis of Google ’ s PageRank

To determine the order in which to display web pages, the search engine Google computes the PageRank vector, whose entries are the PageRanks of the web pages. The PageRank vector is the stationary distribution of a stochastic matrix, the Google matrix. The Google matrix in turn is a convex combination of two stochastic matrices: one matrix represents the link structure of the web graph and a second, rank-one matrix, mimics the random behaviour of web surfers and can also be used to combat web spamming. As a consequence, PageRank depends mainly the link structure of the web graph, but not on the contents of the web pages. We analyze the sensitivity of PageRank to changes in the Google matrix, including addition and deletion of links in the web graph. Due to the proliferation of web pages, the dimension of the Google matrix most likely exceeds ten billion. One of the simplest and most storage-efficient methods for computing PageRank is the power method. We present error bounds for the iterates of the power method and for their residuals. Palabras clave : Markov matrix, stochastic matrix, stationary distribution, power method, perturbation bounds Clasificación por materias AMS : 15A51,65C40,65F15,65F50,65F10