On the convergence of the minimally irreducible Markov chain method with applications to PageRank

PageRank is an important technique for determining the most important nodes in the Web. In this paper, we point out that the main result derived in Bao and Zhu [Acta Math Appl Sin (Engl Ser) 22:517-528, 2006] is incorrect, and establish new lower and upper bounds on the convergence of the minimally irreducible Markov chain method for PageRank. We show that the asymptotic convergence rates of the maximally and the minimally irreducible Markov chains are the same when the damping factor , however, they are not mathematically equivalent any more as . Numerical experiments validate our theoretical results.