Hubs-biased resistance distances on graphs and networks

We define and study two new kinds of ``effective resistances'' based on hubs-biased --hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances between the vertices of a graph. They can be expressed...

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Detalles Bibliográficos
Autores: Estrada, Ernesto, Mugnolo, Delio
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/247551
Acceso en línea:http://hdl.handle.net/10261/247551
Access Level:acceso abierto
Palabra clave:Graph Laplacians
Resistance distances
Spectral properties
Algebraic connectivity
Complex networks
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spelling Hubs-biased resistance distances on graphs and networksEstrada, ErnestoMugnolo, DelioGraph LaplaciansResistance distancesSpectral propertiesAlgebraic connectivityComplex networksWe define and study two new kinds of ``effective resistances'' based on hubs-biased --hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances between the vertices of a graph. They can be expressed in terms of the Moore-Penrose pseudoinverse of the hubs-biased Laplacian matrices of the graph. We define the analogous of the Kirchhoff indices of the graph based of these resistance distances. We prove several results for the new resistance distances and the Kirchhoff indices based on spectral properties of the corresponding Laplacians. After an intensive computational search we conjecture that the Kirchhoff index based on the hubs-repelling resistance distance is not smaller than that based on the standard resistance distance, and that the last is not smaller than the one based on the hubs-attracting resistance distance. We also observe that in real-world brain and neural systems the efficiency of standard random walk processes is as high as that of hubs-attracting schemes. On the contrary, infrastructures and modular software networks seem to be designed to be navigated by using their hubs.The work of D.M. was supported by the Deutsche Forschungsgemeinschaft (Grant 397230547). EE thanks financial support from Ministerio de Ciencia, Innovacion y Universidades, Spain for the grant PID2019-107603GB-I00 “Hubs-repelling/attracting Laplacian operators and related dynamics on graphs/networks”. Both authors acknowledge that this article is based upon work from COST Action CA18232 MAT-DYN-NET, supported by COST (European Cooperation in Science and Technology), www.cost.eu.NoarXivGerman Research FoundationMinisterio de Ciencia, Innovación y Universidades (España)Agencia Estatal de Investigación (España)European CommissionConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202120212021info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/247551reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107603GB-I00https://doi.org/10.48550/arXiv.2101.07103Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2475512026-05-22T06:33:51Z
dc.title.none.fl_str_mv Hubs-biased resistance distances on graphs and networks
title Hubs-biased resistance distances on graphs and networks
spellingShingle Hubs-biased resistance distances on graphs and networks
Estrada, Ernesto
Graph Laplacians
Resistance distances
Spectral properties
Algebraic connectivity
Complex networks
title_short Hubs-biased resistance distances on graphs and networks
title_full Hubs-biased resistance distances on graphs and networks
title_fullStr Hubs-biased resistance distances on graphs and networks
title_full_unstemmed Hubs-biased resistance distances on graphs and networks
title_sort Hubs-biased resistance distances on graphs and networks
dc.creator.none.fl_str_mv Estrada, Ernesto
Mugnolo, Delio
author Estrada, Ernesto
author_facet Estrada, Ernesto
Mugnolo, Delio
author_role author
author2 Mugnolo, Delio
author2_role author
dc.contributor.none.fl_str_mv German Research Foundation
Ministerio de Ciencia, Innovación y Universidades (España)
Agencia Estatal de Investigación (España)
European Commission
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Graph Laplacians
Resistance distances
Spectral properties
Algebraic connectivity
Complex networks
topic Graph Laplacians
Resistance distances
Spectral properties
Algebraic connectivity
Complex networks
description We define and study two new kinds of ``effective resistances'' based on hubs-biased --hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances between the vertices of a graph. They can be expressed in terms of the Moore-Penrose pseudoinverse of the hubs-biased Laplacian matrices of the graph. We define the analogous of the Kirchhoff indices of the graph based of these resistance distances. We prove several results for the new resistance distances and the Kirchhoff indices based on spectral properties of the corresponding Laplacians. After an intensive computational search we conjecture that the Kirchhoff index based on the hubs-repelling resistance distance is not smaller than that based on the standard resistance distance, and that the last is not smaller than the one based on the hubs-attracting resistance distance. We also observe that in real-world brain and neural systems the efficiency of standard random walk processes is as high as that of hubs-attracting schemes. On the contrary, infrastructures and modular software networks seem to be designed to be navigated by using their hubs.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/247551
url http://hdl.handle.net/10261/247551
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107603GB-I00
https://doi.org/10.48550/arXiv.2101.07103
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv arXiv
publisher.none.fl_str_mv arXiv
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
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