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. ISSN 1471-2962 (In Press)

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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 ORCID logoORCID: https://orcid.org/0000-0001-5473-7284, Higham, Desmond J. and Noferini, Vanni;
    Item type:Article
    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:02 Jul 2020 02:39
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/71648
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