Ward, JA orcid.org/0000-0002-2469-7768 (2021) Dimension-reduction of dynamics on real-world networks with symmetry. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2251). 20210026. ISSN 1364-5021
Abstract
We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a large-scale study of such symmetry-induced lumping in real-world networks, from which we identify specific networks for which lumping enables exact analysis that could not have been done on the full state-space. For most networks, lumping gives a state-space compression ratio of up to 10⁷, but the largest compression ratio identified is nearly 10¹². Many of the highest compression ratios occur in animal social networks. We also present examples of types of symmetry found in real-world networks that have not been previously reported.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © 2021 The Author(s). Published by the Royal Society. All rights reserved. This is an author produced version of an article published in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | lumping; networks; data; dynamics; symmetry |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Jun 2021 12:08 |
Last Modified: | 03 Sep 2021 01:54 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rspa.2021.0026 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175500 |