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Dimensionality reduction and spectral properties of multilayer networks

Dimensionality reduction and spectral properties of multilayer networks
Dimensionality reduction and spectral properties of multilayer networks
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered systems include multiple subsystems and layers of connectivity. This new paradigm has attracted a great deal of attention and one fundamental challenge is to characterize multilayer networks both structurally and dynamically. One way to address this question is to study the spectral properties of such networks. Here, we apply the framework of graph quotients, which occurs naturally in this context, and the associated eigenvalue interlacing results, to the adjacency and Laplacian matrices of undirected multilayer networks. Specifically, we describe relationships between the eigenvalue spectra of multilayer networks and their two most natural quotients, the network of layers and the aggregate network, and show the dynamical implications of working with either of the two simplified representations. Our work thus contributes in particular to the study of dynamical processes whose critical properties are determined by the spectral properties of the underlying network.
1539-3755
Sanchez-Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Cozzo, Emanuele
c3d8e86b-ea75-4a30-aa48-01d52cf66045
Moreno, Yamir
55e3a826-d4e5-41d9-a04b-539a82fe5ba0
Sanchez-Garcia, Ruben
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Cozzo, Emanuele
c3d8e86b-ea75-4a30-aa48-01d52cf66045
Moreno, Yamir
55e3a826-d4e5-41d9-a04b-539a82fe5ba0

Sanchez-Garcia, Ruben, Cozzo, Emanuele and Moreno, Yamir (2014) Dimensionality reduction and spectral properties of multilayer networks. Physical Review E. (doi:10.1103/PhysRevE.89.052815).

Record type: Article

Abstract

Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered systems include multiple subsystems and layers of connectivity. This new paradigm has attracted a great deal of attention and one fundamental challenge is to characterize multilayer networks both structurally and dynamically. One way to address this question is to study the spectral properties of such networks. Here, we apply the framework of graph quotients, which occurs naturally in this context, and the associated eigenvalue interlacing results, to the adjacency and Laplacian matrices of undirected multilayer networks. Specifically, we describe relationships between the eigenvalue spectra of multilayer networks and their two most natural quotients, the network of layers and the aggregate network, and show the dynamical implications of working with either of the two simplified representations. Our work thus contributes in particular to the study of dynamical processes whose critical properties are determined by the spectral properties of the underlying network.

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e-pub ahead of print date: 29 May 2014
Published date: May 2014
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 367874
URI: https://eprints.soton.ac.uk/id/eprint/367874
ISSN: 1539-3755
PURE UUID: 5e635bf9-646e-4694-aa90-a6526cf22e3b
ORCID for Ruben Sanchez-Garcia: ORCID iD orcid.org/0000-0001-6479-3028

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Date deposited: 20 Aug 2014 11:27
Last modified: 19 Nov 2019 01:40

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Contributors

Author: Emanuele Cozzo
Author: Yamir Moreno

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