Dynamic random intersection graph: Dynamic local convergence and giant structure

TL;DR

This paper introduces a dynamic random intersection graph model with communities that switch between active and inactive states, analyzing its degree distribution, local convergence, giant component, and maximum group size.

Contribution

It extends classical models by incorporating dynamic community activity, providing new insights into the evolving structure of such networks.

Findings

Analysis of degree distribution in dynamic setting

Results on local convergence properties

Characterization of giant component emergence

Abstract

Random intersection graphs containing an underlying community structure are a popular choice for modelling 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, giant 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.