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Random intersection graphs with communities

Part of: Combinatorial probability Graph theory Operations research and management science

Published online by Cambridge University Press:  22 November 2021

Remco van der Hofstad Open the ORCID record for Remco van der Hofstad [Opens in a new window] ,
Júlia Komjáthy Open the ORCID record for Júlia Komjáthy [Opens in a new window]  and
Viktória Vadon
Remco van der Hofstad*
Affiliation:
Eindhoven University of Technology
Júlia Komjáthy*
Affiliation:
Delft University of Technology
Viktória Vadon*
Affiliation:
University of Miskolc
*
*Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands. Email address: [email protected]
**Postal address: Department of Applied Mathematics, Delft University of Technology, Postbus 5, 2600AA, Delft, The Netherlands. Email address: [email protected]
***Postal address: Institute of Mathematics, University of Miskolc, Egyetem ut 1, 3515, Miskolc, Hungary. Email address: [email protected]
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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.

Keywords

Random networkscommunity structureoverlapping communitiesrandom intersection graphslocal weak convergence

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs 90B15: Network models, stochastic
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 4 , December 2021 , pp. 1061 - 1089
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Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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