Central Limit Theorem for the Largest Component of Random Intersection Graph
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Published:2022-05-20
Issue:2
Volume:29
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Dong Liang,Hu Zhishui
Abstract
Random intersection graphs are models of random graphs in which each vertex is assigned a subset of objects independently and two vertices are adjacent if their assigned subsets are adjacent. Let $n$ and $m=[\beta n^{\alpha}]$ denote the number of vertices and objects respectively. We get a central limit theorem for the largest component of the random intersection graph $G(n,m,p)$ in the supercritical regime and show that it changes between $\alpha>1$, $\alpha=1$ and $\alpha<1$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics