The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering

In this paper, we study the largest component of the near-critical random intersection graph Gn,m,p with n nodes and m elements, where m=Θn which leads to the fact that the clustering is tunable. We prove that with high probability the size of the largest component in the weakly supercritical random...

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Autores principales:	Shiying Huang, Bin Wang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6faab08876ff4a399700cf6c323a9921
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spelling	oai:doaj.org-article:6faab08876ff4a399700cf6c323a99212021-11-22T01:11:20ZThe Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering2314-478510.1155/2021/2284300https://doaj.org/article/6faab08876ff4a399700cf6c323a99212021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2284300https://doaj.org/toc/2314-4785In this paper, we study the largest component of the near-critical random intersection graph Gn,m,p with n nodes and m elements, where m=Θn which leads to the fact that the clustering is tunable. We prove that with high probability the size of the largest component in the weakly supercritical random intersection graph with tunable clustering on n vertices is of order nϵn, and it is of order ϵ−2nlognϵ3n in the weakly subcritical one, where ϵn⟶0 and n1/3ϵn⟶∞ as n⟶∞.Shiying HuangBin WangHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Shiying Huang Bin Wang The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering
description	In this paper, we study the largest component of the near-critical random intersection graph Gn,m,p with n nodes and m elements, where m=Θn which leads to the fact that the clustering is tunable. We prove that with high probability the size of the largest component in the weakly supercritical random intersection graph with tunable clustering on n vertices is of order nϵn, and it is of order ϵ−2nlognϵ3n in the weakly subcritical one, where ϵn⟶0 and n1/3ϵn⟶∞ as n⟶∞.
format	article
author	Shiying Huang Bin Wang
author_facet	Shiying Huang Bin Wang
author_sort	Shiying Huang
title	The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering
title_short	The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering
title_full	The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering
title_fullStr	The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering
title_full_unstemmed	The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering
title_sort	largest component of near-critical random intersection graph with tunable clustering
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/6faab08876ff4a399700cf6c323a9921
work_keys_str_mv	AT shiyinghuang thelargestcomponentofnearcriticalrandomintersectiongraphwithtunableclustering AT binwang thelargestcomponentofnearcriticalrandomintersectiongraphwithtunableclustering AT shiyinghuang largestcomponentofnearcriticalrandomintersectiongraphwithtunableclustering AT binwang largestcomponentofnearcriticalrandomintersectiongraphwithtunableclustering
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The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering

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