The localization of non-backtracking centrality in networks and its physical consequences

The spectrum of the non-backtracking matrix plays a crucial role in determining various structural and dynamical properties of networked systems, ranging from the threshold in bond percolation and non-recurrent epidemic processes, to community structure, to node importance. Here we calculate the lar...

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Detalhes bibliográficos
Autores: Pastor Satorras, Romualdo|||0000-0002-4051-6007, Castellano, Claudio|||0000-0002-3773-3801
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/341841
Acesso em linha:https://hdl.handle.net/2117/341841
https://dx.doi.org/10.1038/s41598-020-78582-x
Access Level:acceso abierto
Palavra-chave:Critical phenomena (Physics)
Complex networks
Nonlinear phenomena
Phase transitions and critical phenomena
Fenòmens crítics (Física)
Àrees temàtiques de la UPC::Física
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spelling The localization of non-backtracking centrality in networks and its physical consequencesPastor Satorras, Romualdo|||0000-0002-4051-6007Castellano, Claudio|||0000-0002-3773-3801Critical phenomena (Physics)Complex networksNonlinear phenomenaPhase transitions and critical phenomenaFenòmens crítics (Física)Àrees temàtiques de la UPC::FísicaThe spectrum of the non-backtracking matrix plays a crucial role in determining various structural and dynamical properties of networked systems, ranging from the threshold in bond percolation and non-recurrent epidemic processes, to community structure, to node importance. Here we calculate the largest eigenvalue of the non-backtracking matrix and the associated non-backtracking centrality for uncorrelated random networks, finding expressions in excellent agreement with numerical results. We show however that the same formulas do not work well for many real-world networks. We identify the mechanism responsible for this violation in the localization of the non-backtracking centrality on network subgraphs whose formation is highly unlikely in uncorrelated networks, but rather common in real-world structures. Exploiting this knowledge we present an heuristic generalized formula for the largest eigenvalue, which is remarkably accurate for all networks of a large empirical dataset. We show that this newly uncovered localization phenomenon allows to understand the failure of the message-passing prediction for the percolation threshold in many real-world structures.Nature20202020-12-1020212021-03-16journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/341841https://dx.doi.org/10.1038/s41598-020-78582-xreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3418412026-05-27T15:37:01Z
dc.title.none.fl_str_mv The localization of non-backtracking centrality in networks and its physical consequences
title The localization of non-backtracking centrality in networks and its physical consequences
spellingShingle The localization of non-backtracking centrality in networks and its physical consequences
Pastor Satorras, Romualdo|||0000-0002-4051-6007
Critical phenomena (Physics)
Complex networks
Nonlinear phenomena
Phase transitions and critical phenomena
Fenòmens crítics (Física)
Àrees temàtiques de la UPC::Física
title_short The localization of non-backtracking centrality in networks and its physical consequences
title_full The localization of non-backtracking centrality in networks and its physical consequences
title_fullStr The localization of non-backtracking centrality in networks and its physical consequences
title_full_unstemmed The localization of non-backtracking centrality in networks and its physical consequences
title_sort The localization of non-backtracking centrality in networks and its physical consequences
dc.creator.none.fl_str_mv Pastor Satorras, Romualdo|||0000-0002-4051-6007
Castellano, Claudio|||0000-0002-3773-3801
author Pastor Satorras, Romualdo|||0000-0002-4051-6007
author_facet Pastor Satorras, Romualdo|||0000-0002-4051-6007
Castellano, Claudio|||0000-0002-3773-3801
author_role author
author2 Castellano, Claudio|||0000-0002-3773-3801
author2_role author
dc.subject.none.fl_str_mv Critical phenomena (Physics)
Complex networks
Nonlinear phenomena
Phase transitions and critical phenomena
Fenòmens crítics (Física)
Àrees temàtiques de la UPC::Física
topic Critical phenomena (Physics)
Complex networks
Nonlinear phenomena
Phase transitions and critical phenomena
Fenòmens crítics (Física)
Àrees temàtiques de la UPC::Física
description The spectrum of the non-backtracking matrix plays a crucial role in determining various structural and dynamical properties of networked systems, ranging from the threshold in bond percolation and non-recurrent epidemic processes, to community structure, to node importance. Here we calculate the largest eigenvalue of the non-backtracking matrix and the associated non-backtracking centrality for uncorrelated random networks, finding expressions in excellent agreement with numerical results. We show however that the same formulas do not work well for many real-world networks. We identify the mechanism responsible for this violation in the localization of the non-backtracking centrality on network subgraphs whose formation is highly unlikely in uncorrelated networks, but rather common in real-world structures. Exploiting this knowledge we present an heuristic generalized formula for the largest eigenvalue, which is remarkably accurate for all networks of a large empirical dataset. We show that this newly uncovered localization phenomenon allows to understand the failure of the message-passing prediction for the percolation threshold in many real-world structures.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-12-10
2021
2021-03-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/341841
https://dx.doi.org/10.1038/s41598-020-78582-x
url https://hdl.handle.net/2117/341841
https://dx.doi.org/10.1038/s41598-020-78582-x
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Nature
publisher.none.fl_str_mv Nature
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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