{"ID":2891869,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.18652","arxiv_id":"2507.18652","title":"Fixed points of Personalized PageRank centrality: From irreducible to reducible networks","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.","short_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 p...","url_abs":"https://arxiv.org/abs/2507.18652","url_pdf":"https://arxiv.org/pdf/2507.18652v1","authors":"[\"David Aleja\",\"Julio Flores\",\"Eva Primo\",\"Daniel Rodríguez\",\"Miguel Romance\"]","published":"2025-07-22T15:21:09Z","proceeding":"cs.SI","tasks":"[\"cs.SI\"]","methods":"[]","has_code":false}