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Relative, local and global dimension in complex networks

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Title: Relative, local and global dimension in complex networks
Authors: Peach, R
Arnaudon, A
Barahona, M
Item Type: Journal Article
Abstract: Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. To take into account locality, finiteness and discreteness, dynamical processes can be used to probe the space geometry and define its dimension. Here we show that each point in space can be assigned a relative dimension with respect to the source of a diffusive process, a concept that provides a scale-dependent definition for local and global dimension also applicable to networks. To showcase its application to physical systems, we demonstrate that the local dimension of structural protein graphs correlates with structural flexibility, and the relative dimension with respect to the active site uncovers regions involved in allosteric communication. In simple models of epidemics on networks, the relative dimension is predictive of the spreading capability of nodes, and identifies scales at which the graph structure is predictive of infectivity. We further apply our dimension measures to neuronal networks, economic trade, social networks, ocean flows, and to the comparison of random graphs.
Issue Date: 2-Jun-2022
Date of Acceptance: 13-May-2022
URI: http://hdl.handle.net/10044/1/97478
DOI: 10.1038/s41467-022-30705-w
ISSN: 2041-1723
Publisher: Nature Research
Journal / Book Title: Nature Communications
Volume: 13
Copyright Statement: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/N014529/1
EP/T027258/1
Keywords: Epidemics
Neurons
Proteins
Neurons
Proteins
Epidemics
physics.soc-ph
physics.soc-ph
Publication Status: Published
Article Number: ARTN 3088
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Department of Brain Sciences
Faculty of Natural Sciences



This item is licensed under a Creative Commons License Creative Commons