Fixed points of Personalized PageRank centrality: From irreducible to reducible networks
Social and Information Networks
2025-07-28 v1
Abstract
In this paper we analyze the 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 PageRank of a graph is given in terms of the number and nature of its strongly connected components. The method presented includes the use of a feedback-PageRank in order to compute exactly the fixed points following the classic Power's Method in terms of the (left-hand) Perron vector of each strongly connected components.
Cite
@article{arxiv.2507.18652,
title = {Fixed points of Personalized PageRank centrality: From irreducible to reducible networks},
author = {David Aleja and Julio Flores and Eva Primo and Daniel Rodríguez and Miguel Romance},
journal= {arXiv preprint arXiv:2507.18652},
year = {2025}
}
Comments
28 pages, 4 figures