Beyond non-backtracking : non-cycling network centrality measures
Arrigo, Francesca and Higham, Desmond J. and Noferini, Vanni (2020) Beyond non-backtracking : non-cycling network centrality measures. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476 (2235). 20190653. ISSN 1471-2962
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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.
Creators(s): |
Arrigo, Francesca ![]() | Item type: | Article |
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ID code: | 71648 |
Keywords: | centrality index, deformed graph Laplacian, Hashimoto matrix, complex network, matrix polynomial, generating function, Mathematics, Mathematics(all) |
Subjects: | Science > Mathematics |
Department: | Faculty of Science > Mathematics and Statistics |
Depositing user: | Pure Administrator |
Date deposited: | 03 Mar 2020 15:30 |
Last modified: | 27 Jan 2021 09:34 |
URI: | https://strathprints.strath.ac.uk/id/eprint/71648 |
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