Cargando…

Universality class of explosive percolation in Barabási-Albert networks

In this work, we study explosive percolation (EP) in Barabási-Albert (BA) network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For m = 1 we find that the critical point t(c) = 1 which is the maximum possible value of the relative...

Descripción completa

Detalles Bibliográficos
Autores principales: Habib E Islam, MD., Hassan, M. K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565682/
https://www.ncbi.nlm.nih.gov/pubmed/31197174
http://dx.doi.org/10.1038/s41598-019-44446-2
_version_ 1783426697850257408
author Habib E Islam, MD.
Hassan, M. K.
author_facet Habib E Islam, MD.
Hassan, M. K.
author_sort Habib E Islam, MD.
collection PubMed
description In this work, we study explosive percolation (EP) in Barabási-Albert (BA) network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For m = 1 we find that the critical point t(c) = 1 which is the maximum possible value of the relative link density t; Hence we cannot have access to the other phase like percolation in one dimension. However, for m > 1 we find that t(c) decreases with increasing m and the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR. It implies that they all belong to the same universality class like EP in the Erdös-Rényi network. Besides, the critical exponents obey the Rushbrooke inequality α + 2β + γ ≥ 2 but always close to equality.     PACS numbers: 61.43.Hv, 64.60.Ht, 68.03.Fg, 82.70.Dd.
format Online
Article
Text
id pubmed-6565682
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher Nature Publishing Group UK
record_format MEDLINE/PubMed
spelling pubmed-65656822019-06-20 Universality class of explosive percolation in Barabási-Albert networks Habib E Islam, MD. Hassan, M. K. Sci Rep Article In this work, we study explosive percolation (EP) in Barabási-Albert (BA) network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For m = 1 we find that the critical point t(c) = 1 which is the maximum possible value of the relative link density t; Hence we cannot have access to the other phase like percolation in one dimension. However, for m > 1 we find that t(c) decreases with increasing m and the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR. It implies that they all belong to the same universality class like EP in the Erdös-Rényi network. Besides, the critical exponents obey the Rushbrooke inequality α + 2β + γ ≥ 2 but always close to equality.     PACS numbers: 61.43.Hv, 64.60.Ht, 68.03.Fg, 82.70.Dd. Nature Publishing Group UK 2019-06-13 /pmc/articles/PMC6565682/ /pubmed/31197174 http://dx.doi.org/10.1038/s41598-019-44446-2 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Habib E Islam, MD.
Hassan, M. K.
Universality class of explosive percolation in Barabási-Albert networks
title Universality class of explosive percolation in Barabási-Albert networks
title_full Universality class of explosive percolation in Barabási-Albert networks
title_fullStr Universality class of explosive percolation in Barabási-Albert networks
title_full_unstemmed Universality class of explosive percolation in Barabási-Albert networks
title_short Universality class of explosive percolation in Barabási-Albert networks
title_sort universality class of explosive percolation in barabási-albert networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565682/
https://www.ncbi.nlm.nih.gov/pubmed/31197174
http://dx.doi.org/10.1038/s41598-019-44446-2
work_keys_str_mv AT habibeislammd universalityclassofexplosivepercolationinbarabasialbertnetworks
AT hassanmk universalityclassofexplosivepercolationinbarabasialbertnetworks