Ranking Websites: A Probabilistic View

Abstract

In this paper we suggest evaluating the importance of a website with the mean frequency of visiting the website for the Markov chain on the Internet graph describing random surfing. We show that this mean frequency is equal to the sum of the PageRanks of all the webpages in that website (hence referred to as PageRankSum), and we propose a novel algorithm, AggregateRank, based on the theory of stochastic complement to calculate the rank of a website. The AggregateRank algorithm gives a good approximation of the PageRankSum accurately, while the corresponding computational complexity is much lower than PageRankSum. By constructing return-time Markov chains restricted to each website, we describe also the probabilistic relation between PageRank and AggregateRank. The complexity of the AggregateRank algorithm, the error bound of the estimation, and the experiments are discussed at the end of the paper.