On some analytical properties of a general PageRank algorithm

In this study, we present a theoretical analysis of some properties of a general algorithm for computation of the PageRank vector. It is shown that the convergence to the PageRank vector is generally nonuniform. Expressions for the limiting forms of the principal matrix of the PageRank approximation and the PageRank vector are derived in terms of the original stochastic matrix and the personalization vector. Some implications of the obtained results for ranking web pages are discussed.