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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2284300 |
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| _version_ | 1832550980094263296 |
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| author | Shiying Huang Bin Wang |
| author_facet | Shiying Huang Bin Wang |
| author_sort | Shiying Huang |
| collection | DOAJ |
| 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 |
| id | doaj-art-6faab08876ff4a399700cf6c323a9921 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6faab08876ff4a399700cf6c323a99212025-02-03T06:05:16ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/2284300The Largest Component of Near-Critical Random Intersection Graph with Tunable ClusteringShiying Huang0Bin Wang1School of Mathematics and Computational ScienceCollege of ScienceIn 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⟶∞.http://dx.doi.org/10.1155/2021/2284300 |
| spellingShingle | Shiying Huang Bin Wang The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering Journal of Mathematics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2021/2284300 |
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