Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model

This paper presents a new method of filtering graphs to check exact graph isomorphism and extracting their mapping. Each graph is modeled by a resistive electrical circuit using the Conductance Electrical Model (CEM). By using this model, a necessary condition to check the isomorphism of two graphs...

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Detalles Bibliográficos
Autores: Igelmo, Manuel, Sanfeliu, Alberto
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2016
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/132969
Acceso en línea:http://hdl.handle.net/10261/132969
Access Level:acceso abierto
Palabra clave:Graph isomorphism
Graph matching
Conductances equivalent model
Star method
Graph filter
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spelling Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical ModelIgelmo, ManuelSanfeliu, AlbertoSanfeliu, AlbertoGraph isomorphismGraph matchingConductances equivalent modelStar methodGraph filterThis paper presents a new method of filtering graphs to check exact graph isomorphism and extracting their mapping. Each graph is modeled by a resistive electrical circuit using the Conductance Electrical Model (CEM). By using this model, a necessary condition to check the isomorphism of two graphs is that their equivalent resistances have the same values, but this is not enough, and we have to look for their mapping to find the sufficient condition. We can compute the isomorphism between two graphs in O(N3), where N is the order of the graph, if their star resistance values are different, otherwise the computational time is exponential, but only with respect to the number of repeated star resistance values, which usually is very small. We can use this technique to filter graphs that are not isomorphic and in case that they are, we can obtain their node mapping. A distinguishing feature over other methods is that, even if there exists repeated star resistance values, we can extract a partial node mapping (of all the nodes except the repeated ones and their neighbors) in O(N3). The paper presents the method and its application to detect isomorphic graphs in two well know graph databases, where some graphs have more than 600 nodes.This work was partially funded by CICYT DPI2013-42458-P.Peer reviewedElsevierMinisterio de Economía y Competitividad (España)Comisión Interministerial de Ciencia y Tecnología, CICYT (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]201620162016info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/132969reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/DPI2013-42458-Phttp://dx.doi.org/10.1016/j.patcog.2016.03.015Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1329692026-05-22T06:33:51Z
dc.title.none.fl_str_mv Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
title Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
spellingShingle Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
Igelmo, Manuel
Graph isomorphism
Graph matching
Conductances equivalent model
Star method
Graph filter
title_short Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
title_full Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
title_fullStr Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
title_full_unstemmed Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
title_sort Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
dc.creator.none.fl_str_mv Igelmo, Manuel
Sanfeliu, Alberto
Sanfeliu, Alberto
author Igelmo, Manuel
author_facet Igelmo, Manuel
Sanfeliu, Alberto
author_role author
author2 Sanfeliu, Alberto
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
Comisión Interministerial de Ciencia y Tecnología, CICYT (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Graph isomorphism
Graph matching
Conductances equivalent model
Star method
Graph filter
topic Graph isomorphism
Graph matching
Conductances equivalent model
Star method
Graph filter
description This paper presents a new method of filtering graphs to check exact graph isomorphism and extracting their mapping. Each graph is modeled by a resistive electrical circuit using the Conductance Electrical Model (CEM). By using this model, a necessary condition to check the isomorphism of two graphs is that their equivalent resistances have the same values, but this is not enough, and we have to look for their mapping to find the sufficient condition. We can compute the isomorphism between two graphs in O(N3), where N is the order of the graph, if their star resistance values are different, otherwise the computational time is exponential, but only with respect to the number of repeated star resistance values, which usually is very small. We can use this technique to filter graphs that are not isomorphic and in case that they are, we can obtain their node mapping. A distinguishing feature over other methods is that, even if there exists repeated star resistance values, we can extract a partial node mapping (of all the nodes except the repeated ones and their neighbors) in O(N3). The paper presents the method and its application to detect isomorphic graphs in two well know graph databases, where some graphs have more than 600 nodes.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016
2016
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/10261/132969
url http://hdl.handle.net/10261/132969
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/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/DPI2013-42458-P
http://dx.doi.org/10.1016/j.patcog.2016.03.015
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
repository.mail.fl_str_mv
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score 15.811543

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