Fixed points of personalized PageRank centrality: From irreducible to reducible networks

Abstract

In this paper we analyze PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of the PageRank of a graph is given in terms of the number and nature of its strongly connected components. The method presented essentially follows the classic Power's Method by means of a feedback-PageRank that allows to precisely compute the fixed points, in terms of the (left-hand) Perron vector of each strongly connected component. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).