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Spectral density of equitable core-periphery graphs

Barucca, P; (2020) Spectral density of equitable core-periphery graphs. Physica A: Statistical Mechanics and its Applications , 553 , Article 124649. 10.1016/j.physa.2020.124649. Green open access

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Abstract

Core-periphery structure is an emerging property of a wide range of complex systems and indicate the presence of group of actors in the system with an higher number of connections among them and a lower number of connections with a sparsely connected periphery. The dynamics of a complex system which is interacting on a given graph structure is strictly connected with the spectral properties of the graph itself, nevertheless it is generally extremely hard to obtain analytic results which will hold for arbitrary large systems. Recently a statistical ensemble of random graphs with a regular block structure, i.e. the ensemble of equitable graphs, has been introduced and analytic results have been derived in the computationally-hard context of graph partitioning and community detection. In this paper, we present a general analytic result for a ensemble of equitable core-periphery graphs, yielding a new explicit formula for the spectral density of networks with core-periphery structure.

Type: Article
Title: Spectral density of equitable core-periphery graphs
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.physa.2020.124649
Publisher version: https://doi.org/10.1016/j.physa.2020.124649
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: network theory, core-periphery, spectral theory, cavity method
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10074324
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