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...
Autores principales: | , |
---|---|
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 |