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 (https://doi.org/10.1098/rspa.2019.0653)

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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.

ORCID iDs

Arrigo, Francesca ORCID logoORCID: https://orcid.org/0000-0001-5473-7284, Higham, Desmond J. and Noferini, Vanni;
  • Item type:Article
    ID code:71648
    Dates:
    Date
    Event
    25 March 2020
    Published
    11 March 2020
    Published Online
    12 February 2020
    Accepted
    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:29 Jun 2022 01:30
    URI:https://strathprints.strath.ac.uk/id/eprint/71648
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