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Exploiting symmetry in network analysis

Exploiting symmetry in network analysis
Exploiting symmetry in network analysis
Virtually all network analyses involve structural measures between pairs of vertices, or of the vertices themselves, and the large amount of symmetry present in real-world complex networks is inherited and often amplified by such measures. This has practical consequences which have not yet been explored in full generality, nor systematically exploited by network practitioners. Here we present a general and comprehensive study of the effect of network symmetry on arbitrary network measures, and show how this can be exploited in practice in a number of ways, from redundancy compression, to computational reduction. We also uncover the spectral signatures of symmetry for an arbitrary network measure such as the graph Laplacian. Computing network symmetries is very efficient in practice, and we test real-world examples up to several million nodes. Since network models are ubiquitous in the Applied Sciences, and typically contain a large degree of structural redundancy, our results are not only significant, but widely applicable.
2399-3650
1-17
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Sanchez Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed

Sanchez Garcia, Ruben (2020) Exploiting symmetry in network analysis. Communications Physics, 1-17. (In Press)

Record type: Article

Abstract

Virtually all network analyses involve structural measures between pairs of vertices, or of the vertices themselves, and the large amount of symmetry present in real-world complex networks is inherited and often amplified by such measures. This has practical consequences which have not yet been explored in full generality, nor systematically exploited by network practitioners. Here we present a general and comprehensive study of the effect of network symmetry on arbitrary network measures, and show how this can be exploited in practice in a number of ways, from redundancy compression, to computational reduction. We also uncover the spectral signatures of symmetry for an arbitrary network measure such as the graph Laplacian. Computing network symmetries is very efficient in practice, and we test real-world examples up to several million nodes. Since network models are ubiquitous in the Applied Sciences, and typically contain a large degree of structural redundancy, our results are not only significant, but widely applicable.

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More information

Submitted date: 9 July 2018
Accepted/In Press date: 30 March 2020

Identifiers

Local EPrints ID: 430615
URI: http://eprints.soton.ac.uk/id/eprint/430615
ISSN: 2399-3650
PURE UUID: 456151f2-c571-4708-a8ec-eb9ebfe21fc5
ORCID for Ruben Sanchez Garcia: ORCID iD orcid.org/0000-0001-6479-3028

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Date deposited: 07 May 2019 16:30
Last modified: 13 Dec 2021 03:04

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