Centrality measures in simplicial complexes: Applications of topological data analysis to network science

[EN]Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for si...

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Autores: Hernández Serrano, Daniel, Sánchez Gómez, Darío
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/161855
Acceso en línea:http://hdl.handle.net/10366/161855
Access Level:acceso abierto
Palabra clave:Complex networks
Simplicial complexes
Topological data analysis
Network science
Statistical mechanics
12 Matemáticas
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spelling Centrality measures in simplicial complexes: Applications of topological data analysis to network scienceHernández Serrano, DanielSánchez Gómez, DaríoComplex networksSimplicial complexesTopological data analysisNetwork scienceStatistical mechanics12 Matemáticas[EN]Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for simplices need to be proposed. Many of the classical complex networks centralities are based on the degree of a node, so in order to define degree centrality measures for simplices (which would characterise the relevance of a simplicial community in a simplicial network), a different definition of adjacency between simplices is required, since, contrarily to what happens in the vertex case (where there is only upper adjacency), simplices might also have other types of adjacency. The aim of these notes is threefold: first we will use the recently introduced notions of higher order simplicial degrees to propose new degree based centrality measures in simplicial complexes. These theoretical centrality measures, such as the simplicial degree centrality or the eigenvector centrality would allow not only to study the relevance of a simplicial community and the quality of its higher-order connections in a simplicial network, but also they might help to elucidate topological and dynamical properties of simplicial networks; sencond, we define notions of walks and distances in simplicial complexes in order to study connectivity of simplicial networks and to generalise, to the simplicial case, the well known closeness and betweenness centralities (needed for instance to study the relevance of a simplicial community in terms of its ability of transmitting information); third, we propose a new clustering coefficient for simplices in a simplicial network, different from the one knows so far and which generalises the standard graph clustering of a vertex. This measure should be essential to know the density of a simplicial network in terms of its simplicial communities.This work has been supported by Ministerio de Economía y Competitividad (Spain) and the European Union through FEDER funds under grants TIN2017-84844-C2-2-R and MTM2017-86042-P, and the project STAMGAD 18.J445 / 463AC03 supported by Consejería de Educación (GIR, Junta de Castilla y León, Spain).0096-3003/© 2020 Elsevier Inc. All rights reserved. Publicado bajo acuerdo APC y versión final publicada aquí bajo el permiso del Open Access Support Team de la editorial Elsevier.Elsevier202520252020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10366/161855reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésTIN2017-84844-C2-2-RMTM2017-86042-PSTAMGAD 18.J445Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1618552026-06-07T06:28:51Z
dc.title.none.fl_str_mv Centrality measures in simplicial complexes: Applications of topological data analysis to network science
title Centrality measures in simplicial complexes: Applications of topological data analysis to network science
spellingShingle Centrality measures in simplicial complexes: Applications of topological data analysis to network science
Hernández Serrano, Daniel
Complex networks
Simplicial complexes
Topological data analysis
Network science
Statistical mechanics
12 Matemáticas
title_short Centrality measures in simplicial complexes: Applications of topological data analysis to network science
title_full Centrality measures in simplicial complexes: Applications of topological data analysis to network science
title_fullStr Centrality measures in simplicial complexes: Applications of topological data analysis to network science
title_full_unstemmed Centrality measures in simplicial complexes: Applications of topological data analysis to network science
title_sort Centrality measures in simplicial complexes: Applications of topological data analysis to network science
dc.creator.none.fl_str_mv Hernández Serrano, Daniel
Sánchez Gómez, Darío
author Hernández Serrano, Daniel
author_facet Hernández Serrano, Daniel
Sánchez Gómez, Darío
author_role author
author2 Sánchez Gómez, Darío
author2_role author
dc.subject.none.fl_str_mv Complex networks
Simplicial complexes
Topological data analysis
Network science
Statistical mechanics
12 Matemáticas
topic Complex networks
Simplicial complexes
Topological data analysis
Network science
Statistical mechanics
12 Matemáticas
description [EN]Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for simplices need to be proposed. Many of the classical complex networks centralities are based on the degree of a node, so in order to define degree centrality measures for simplices (which would characterise the relevance of a simplicial community in a simplicial network), a different definition of adjacency between simplices is required, since, contrarily to what happens in the vertex case (where there is only upper adjacency), simplices might also have other types of adjacency. The aim of these notes is threefold: first we will use the recently introduced notions of higher order simplicial degrees to propose new degree based centrality measures in simplicial complexes. These theoretical centrality measures, such as the simplicial degree centrality or the eigenvector centrality would allow not only to study the relevance of a simplicial community and the quality of its higher-order connections in a simplicial network, but also they might help to elucidate topological and dynamical properties of simplicial networks; sencond, we define notions of walks and distances in simplicial complexes in order to study connectivity of simplicial networks and to generalise, to the simplicial case, the well known closeness and betweenness centralities (needed for instance to study the relevance of a simplicial community in terms of its ability of transmitting information); third, we propose a new clustering coefficient for simplices in a simplicial network, different from the one knows so far and which generalises the standard graph clustering of a vertex. This measure should be essential to know the density of a simplicial network in terms of its simplicial communities.
publishDate 2020
dc.date.none.fl_str_mv 2020
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/161855
url http://hdl.handle.net/10366/161855
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv TIN2017-84844-C2-2-R
MTM2017-86042-P
STAMGAD 18.J445
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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