Analytic solution of the two-star model with correlated degrees
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/233035 |
Resumo: | Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the degrees of adjacent nodes (nearest neighbors) and between the degrees at the end-points of two-stars (next nearest neighbors). We compute exactly the network free energy and show that this model undergoes a first-order transition to a condensed phase. For non-negative degree correlations between next nearest neighbors, the degree distribution inside the condensed phase has a single peak at the largest degree, while for negative degree correlations between next nearest neighbors the condensed phase is characterized by a bimodal degree distribution. We calculate the degree assortativities and show they are nonmonotonic functions of the model parameters, with a discontinuous behavior at the first-order transition. The first-order critical line terminates at a second-order critical point, whose location in the phase diagram can be accurately determined. Our results can help to develop more detailed models of complex networks with correlated degrees. |
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Bolfe, Maíra AngélicaMetz, Fernando LucasGuzmán-González, EdgarPérez-Castillo, Isaac2021-12-17T04:30:12Z20211539-3755http://hdl.handle.net/10183/233035001129900Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the degrees of adjacent nodes (nearest neighbors) and between the degrees at the end-points of two-stars (next nearest neighbors). We compute exactly the network free energy and show that this model undergoes a first-order transition to a condensed phase. For non-negative degree correlations between next nearest neighbors, the degree distribution inside the condensed phase has a single peak at the largest degree, while for negative degree correlations between next nearest neighbors the condensed phase is characterized by a bimodal degree distribution. We calculate the degree assortativities and show they are nonmonotonic functions of the model parameters, with a discontinuous behavior at the first-order transition. The first-order critical line terminates at a second-order critical point, whose location in the phase diagram can be accurately determined. Our results can help to develop more detailed models of complex networks with correlated degrees.application/pdfengPhysical review. E, Statistical, nonlinear, and soft matter physics. Melville. Vol. 104, no. 1 (July 2021), 014147, 13 p.Diagramas de faseRedes complexasDistribuicao de poissonAnalytic solution of the two-star model with correlated degreesEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001129900.pdf.txt001129900.pdf.txtExtracted Texttext/plain55958http://www.lume.ufrgs.br/bitstream/10183/233035/2/001129900.pdf.txt800c6e0922024b50cd5560c84f16b359MD52ORIGINAL001129900.pdfTexto completo (inglês)application/pdf1024831http://www.lume.ufrgs.br/bitstream/10183/233035/1/001129900.pdf02aef68646bd6d36af594f81edded879MD5110183/2330352023-05-21 03:27:26.93433oai:www.lume.ufrgs.br:10183/233035Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-05-21T06:27:26Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Analytic solution of the two-star model with correlated degrees |
title |
Analytic solution of the two-star model with correlated degrees |
spellingShingle |
Analytic solution of the two-star model with correlated degrees Bolfe, Maíra Angélica Diagramas de fase Redes complexas Distribuicao de poisson |
title_short |
Analytic solution of the two-star model with correlated degrees |
title_full |
Analytic solution of the two-star model with correlated degrees |
title_fullStr |
Analytic solution of the two-star model with correlated degrees |
title_full_unstemmed |
Analytic solution of the two-star model with correlated degrees |
title_sort |
Analytic solution of the two-star model with correlated degrees |
author |
Bolfe, Maíra Angélica |
author_facet |
Bolfe, Maíra Angélica Metz, Fernando Lucas Guzmán-González, Edgar Pérez-Castillo, Isaac |
author_role |
author |
author2 |
Metz, Fernando Lucas Guzmán-González, Edgar Pérez-Castillo, Isaac |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Bolfe, Maíra Angélica Metz, Fernando Lucas Guzmán-González, Edgar Pérez-Castillo, Isaac |
dc.subject.por.fl_str_mv |
Diagramas de fase Redes complexas Distribuicao de poisson |
topic |
Diagramas de fase Redes complexas Distribuicao de poisson |
description |
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the degrees of adjacent nodes (nearest neighbors) and between the degrees at the end-points of two-stars (next nearest neighbors). We compute exactly the network free energy and show that this model undergoes a first-order transition to a condensed phase. For non-negative degree correlations between next nearest neighbors, the degree distribution inside the condensed phase has a single peak at the largest degree, while for negative degree correlations between next nearest neighbors the condensed phase is characterized by a bimodal degree distribution. We calculate the degree assortativities and show they are nonmonotonic functions of the model parameters, with a discontinuous behavior at the first-order transition. The first-order critical line terminates at a second-order critical point, whose location in the phase diagram can be accurately determined. Our results can help to develop more detailed models of complex networks with correlated degrees. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-12-17T04:30:12Z |
dc.date.issued.fl_str_mv |
2021 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/233035 |
dc.identifier.issn.pt_BR.fl_str_mv |
1539-3755 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001129900 |
identifier_str_mv |
1539-3755 001129900 |
url |
http://hdl.handle.net/10183/233035 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear, and soft matter physics. Melville. Vol. 104, no. 1 (July 2021), 014147, 13 p. |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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application/pdf |
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reponame:Repositório Institucional da UFRGS instname:Universidade Federal do Rio Grande do Sul (UFRGS) instacron:UFRGS |
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