Beyond non-backtracking: non-cycling network centrality measures

Author:

Arrigo Francesca1,Higham Desmond J.2,Noferini Vanni3ORCID

Affiliation:

1. Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK

2. School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3FD, UK

3. Department of Mathematics and Systems Analysis, Aalto University, PO Box 11100, 00076 Aalto, Finland

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.

Funder

Engineering and Physical Sciences Research Council

Leverhulme Trust

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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1. Generating functions of non-backtracking walks on weighted digraphs: Radius of convergence and Ihara's theorem;Linear Algebra and its Applications;2024-10

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3. Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs;SIAM Journal on Matrix Analysis and Applications;2024-01-30

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