Random bipartite graphs with i.i.d. weights and applications to inhomogeneous random intersection graphs

2025/03/20 by Alastair Haig, Haig, Alastair, Minmin Wang +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2503.16688

openalex publication_date 2025/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection graph which has nontrivial clustering properties and inhomogeneous vertex degrees. We focus on the situation where the weights are themselves i.i.d. random variables. In the so-called moderate clustering regime, we identify three types of scaling limit for the large connected components in the graphs at criticality, depending on the tail behaviours of the weight distributions of both parts.

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