PageRank and Perturbed Markov Chains

PageRank is a widely used hyperlink‐based algorithm for estimating the relative importance of nodes in networks. In this chapter, the authors formulate the PageRank problem as a first‐ and second‐order Markov chains perturbation problem. Using numerical experiments, they compare convergence rates for different values of perturbation parameter on different graph structures and investigate the difference in ranks for the two problems. Generally, the PageRank problem of the second‐order perturbed Markov chains can be seen as a way to control over‐scoring of some vertices when strategic promotion is made. The authors conclude that the second‐order perturbed Markov chain cannot be ignored since it is practically advantageous when strategic promotion is required.