Dynamic Random Intersection Graph: Dynamic Local Convergence and Giant Structure

Marta Milewska; Remco van der Hofstad; Bert Zwart

doi:10.1002/rsa.21264

Dynamic Random Intersection Graph: Dynamic Local Convergence and Giant Structure

Marta Milewska (Corresponding author), Remco van der Hofstad, Bert Zwart

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Abstract

Random intersection graphs containing an underlying community structure are a popular choice for modeling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when they share at least one group. We extend this approach and make the communities dynamic by letting them alternate between an active and inactive phase. We analyse the new model, delivering results on degree distribution, local convergence, largest connected component, and maximum group size, paying particular attention to the dynamic description of these properties. We also describe the connection between our model and the bipartite configuration model, which is of independent interest.

Original language	English
Article number	e21264
Number of pages	38
Journal	Random Structures and Algorithms
Volume	66
Issue number	1
DOIs	https://doi.org/10.1002/rsa.21264
Publication status	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Random Structures & Algorithms published by Wiley Periodicals LLC.

Funding

Funders	Funder number
Marie Skłodowska‐Curie
European Union's Horizon 2020 - Research and Innovation Framework Programme
European Union's Horizon 2020 - Research and Innovation Framework Programme	945045
NWO	024.002.003

Keywords

bipartite generalized random graph
dynamic largest connected component process
dynamic local convergence
random intersection graphs

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10.1002/rsa.21264

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Dynamic Random Intersection Graph: Dynamic Local Convergence and Giant Structure

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