Random intersection graphs with communities

Journal article (2021)

Authors

Remco Van Der Hofstad Eindhoven University of Technology

J. Komjáthy Applied Probability -

Viktória Vadon University of Miskolc

Research Group

Applied Probability () (TU Delft)

Community structure Overlapping communities Random intersection graphs Local weak convergence Random networks

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http://resolver.tudelft.nl/uuid:476bd8de-c9e3-46a6-b0b2-480db76f0c76

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.

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