Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component

Autores
Di Muro, Matias Alberto; Valdez, Lucas Daniel; Stanley, Harry Eugene; Buldyrev, Sergey V.; Braunstein, Lidia Adriana
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested in recent years that they could be complementary. In this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k-core percolation and vice versa, if the functionality thresholds in both processes satisfy a complementary relation. Another interesting problem in bootstrap and k-core percolation is the fraction of nodes belonging to their giant connected components P∞b and P∞c, respectively. We solve this problem analytically for arbitrary randomly connected graphs and arbitrary threshold distributions, and we show that P∞b and P∞c are not complementary. Our theoretical results coincide with computer simulations in the limit of very large graphs. In bootstrap percolation, we show that when using the branching theory to compute the size of the giant component, we must consider two different types of links, which are related to distinct spanning branches of active nodes.
Fil: Di Muro, Matias Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Valdez, Lucas Daniel. Boston University; Estados Unidos
Fil: Stanley, Harry Eugene. Boston University; Estados Unidos
Fil: Buldyrev, Sergey V.. Yeshiva University; Estados Unidos
Fil: Braunstein, Lidia Adriana. Politecnico di Milano; Italia
Materia
Complex Networks
Percolation
Bootstrap
k-core
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/122919
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant componentDi Muro, Matias AlbertoValdez, Lucas DanielStanley, Harry EugeneBuldyrev, Sergey V.Braunstein, Lidia AdrianaComplex NetworksPercolationBootstrapk-corehttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested in recent years that they could be complementary. In this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k-core percolation and vice versa, if the functionality thresholds in both processes satisfy a complementary relation. Another interesting problem in bootstrap and k-core percolation is the fraction of nodes belonging to their giant connected components P∞b and P∞c, respectively. We solve this problem analytically for arbitrary randomly connected graphs and arbitrary threshold distributions, and we show that P∞b and P∞c are not complementary. Our theoretical results coincide with computer simulations in the limit of very large graphs. In bootstrap percolation, we show that when using the branching theory to compute the size of the giant component, we must consider two different types of links, which are related to distinct spanning branches of active nodes.Fil: Di Muro, Matias Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Valdez, Lucas Daniel. Boston University; Estados UnidosFil: Stanley, Harry Eugene. Boston University; Estados UnidosFil: Buldyrev, Sergey V.. Yeshiva University; Estados UnidosFil: Braunstein, Lidia Adriana. Politecnico di Milano; ItaliaAmerican Physical Society2019-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/122919Di Muro, Matias Alberto; Valdez, Lucas Daniel; Stanley, Harry Eugene; Buldyrev, Sergey V.; Braunstein, Lidia Adriana; Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component; American Physical Society; Physical Review E; 99; 2; 2-20192470-0045CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevE.99.022311info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.99.022311info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:05:57Zoai:ri.conicet.gov.ar:11336/122919instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:05:57.653CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
title Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
spellingShingle Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
Di Muro, Matias Alberto
Complex Networks
Percolation
Bootstrap
k-core
title_short Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
title_full Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
title_fullStr Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
title_full_unstemmed Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
title_sort Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
dc.creator.none.fl_str_mv Di Muro, Matias Alberto
Valdez, Lucas Daniel
Stanley, Harry Eugene
Buldyrev, Sergey V.
Braunstein, Lidia Adriana
author Di Muro, Matias Alberto
author_facet Di Muro, Matias Alberto
Valdez, Lucas Daniel
Stanley, Harry Eugene
Buldyrev, Sergey V.
Braunstein, Lidia Adriana
author_role author
author2 Valdez, Lucas Daniel
Stanley, Harry Eugene
Buldyrev, Sergey V.
Braunstein, Lidia Adriana
author2_role author
author
author
author
dc.subject.none.fl_str_mv Complex Networks
Percolation
Bootstrap
k-core
topic Complex Networks
Percolation
Bootstrap
k-core
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested in recent years that they could be complementary. In this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k-core percolation and vice versa, if the functionality thresholds in both processes satisfy a complementary relation. Another interesting problem in bootstrap and k-core percolation is the fraction of nodes belonging to their giant connected components P∞b and P∞c, respectively. We solve this problem analytically for arbitrary randomly connected graphs and arbitrary threshold distributions, and we show that P∞b and P∞c are not complementary. Our theoretical results coincide with computer simulations in the limit of very large graphs. In bootstrap percolation, we show that when using the branching theory to compute the size of the giant component, we must consider two different types of links, which are related to distinct spanning branches of active nodes.
Fil: Di Muro, Matias Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Valdez, Lucas Daniel. Boston University; Estados Unidos
Fil: Stanley, Harry Eugene. Boston University; Estados Unidos
Fil: Buldyrev, Sergey V.. Yeshiva University; Estados Unidos
Fil: Braunstein, Lidia Adriana. Politecnico di Milano; Italia
description K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested in recent years that they could be complementary. In this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k-core percolation and vice versa, if the functionality thresholds in both processes satisfy a complementary relation. Another interesting problem in bootstrap and k-core percolation is the fraction of nodes belonging to their giant connected components P∞b and P∞c, respectively. We solve this problem analytically for arbitrary randomly connected graphs and arbitrary threshold distributions, and we show that P∞b and P∞c are not complementary. Our theoretical results coincide with computer simulations in the limit of very large graphs. In bootstrap percolation, we show that when using the branching theory to compute the size of the giant component, we must consider two different types of links, which are related to distinct spanning branches of active nodes.
publishDate 2019
dc.date.none.fl_str_mv 2019-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/122919
Di Muro, Matias Alberto; Valdez, Lucas Daniel; Stanley, Harry Eugene; Buldyrev, Sergey V.; Braunstein, Lidia Adriana; Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component; American Physical Society; Physical Review E; 99; 2; 2-2019
2470-0045
CONICET Digital
CONICET
url http://hdl.handle.net/11336/122919
identifier_str_mv Di Muro, Matias Alberto; Valdez, Lucas Daniel; Stanley, Harry Eugene; Buldyrev, Sergey V.; Braunstein, Lidia Adriana; Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component; American Physical Society; Physical Review E; 99; 2; 2-2019
2470-0045
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevE.99.022311
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.99.022311
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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