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

Shiying Huang | Zendy; Bin Wang | Zendy

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

Author(s) -

Shiying Huang,

Bin Wang

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/2284300

Subject(s) - mathematics , intersection graph , component (thermodynamics) , combinatorics , cluster analysis , connected component , graph , intersection (aeronautics) , discrete mathematics , line graph , statistics , geography , cartography , physics , thermodynamics

In this paper, we study the largest component of the near-critical random intersection graph G n , m , p with n nodes and m elements, where m = Θ n 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 n ϵ n , and it is of order ϵ − 2 n log n ϵ 3 n in the weakly subcritical one, where ϵ n ⟶ 0 and n 1 / 3 ϵ n ⟶ ∞ as n ⟶ ∞ .

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