Network Capacity Bound for Personalized PageRank in Multimodal Networks

Article type: Research Article

Authors: Kłopotek, Mieczysław A.^{; *} | Wierzchoń, Sławomir T. | Kłopotek, Robert A.

Affiliations: Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland, klopotek@ipipan.waw.pl

Correspondence: [*] Address for correspondence: Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland.

Abstract: In a former paper [1] the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we deal with a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. We state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.

Keywords: PageRank, random walk, ranking, multimodal networks, social networks, M-uniform M-partite hypegraphs, authority flow bounds

DOI: 10.3233/FI-222151

Journal: Fundamenta Informaticae, vol. 189, no. 1, pp. 49-68, 2022