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 (

[thumbnail of Arrigo-etal-PRS-MPES-2020-non-cycling-network-centrality-measures]
Text. Filename: Arrigo_etal_PRS_MPES_2020_non_cycling_network_centrality_measures.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo

Download (980kB)| Preview


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.