Beyond non-backtracking: non-cycling network centrality measures. (11th March 2020)

• Record Type: Journal Article
• Authors: Arrigo, Francesca; Higham, Desmond J.; Noferini, Vanni
• Is Part Of: Proceedings. Volume 476:Number 2235(2020)
• Publication Date: 2020-03-11
• Subjects: centrality index -- deformed graph Laplacian -- Hashimoto matrix -- complex network -- matrix polynomial -- generating function; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2019.0653
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : Walks around a graph are studied in a wide range of fields, from graph theory and stochastic analysis to theoretical computer science and physics. In many cases it is of interest to focus on non-backtracking walks; those that do not immediately revisit their previous location. In the network science context, imposing a non-backtracking constraint on traditional walk-based node centrality measures is known to offer tangible benefits. Here, we use the Hashimoto matrix construction to characterize, generalize and study such non-backtracking centrality measures. We then devise a recursive extension that systematically removes triangles, squares and, generally, all cycles up to a given length. By characterizing the spectral radius of appropriate matrix power series, we explore how the universality results on the limiting behaviour of classical walk-based centrality measures extend to these non-cycling cases. We also demonstrate that the new recursive construction gives rise to practical centrality measures that can be applied to large-scale networks.