PageRank algorithm and Monte Carlo methods in PageRank Computation

PageRank is the algorithm used by the Google search engine for ranking web pages. PageRank Algorithm calculates for each page a relative importance score which can be interpreted as the frequency of how often a page is visited by a surfer. The purpose of this work is to provide a mathematical analysis of the PageRank Algorithm. We analyze the random surfer model and the linear algebra behind it which complements the discussion of Markov Chains in matrix algebra. We also study Monte Carlo type methods for PageRank computation, which have several advantages over the Power method used by Google: Monte Carlo methods provide good estimation of the PageRank for relatively important pages already after one iteration; Monte Carlo methods have natural parallel implementation; and finally, Monte Carlo methods allow to perform continuous update of the PageRank as the structure of the Web changes.