Random intersection graphs with communities. (December 2021)

• Record Type: Journal Article
• Authors: van der Hofstad, Remco; Komjáthy, Júlia; Vadon, Viktória
• Is Part Of: Advances in applied probability. Volume 53:Number 4(2021)
• Page Start: 1061
• Page End: 1089
• Publication Date: 2021-12
• Subjects: Random networks -- community structure -- overlapping communities -- random intersection graphs -- local weak convergence; 60C05 -- 05C80 -- 90B15; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2021.12
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: Random intersection graphs model networks with communities, assuming an underlying bipartite structure of communities and individuals, where these communities may overlap. We generalize the model, allowing for arbitrary community structures within the communities. In our new model, communities may overlap, and they have their own internal structure described by arbitrary finite community graphs. Our model turns out to be tractable. We analyze the overlapping structure of the communities, show local weak convergence (including convergence of subgraph counts), and derive the asymptotic degree distribution and the local clustering coefficient.