Degree Distributions in General Random Intersection Graphs

TL;DR

This paper analyzes a variant of random intersection graphs where vertex weights influence degree distributions, revealing how individual and collective weight distributions affect connectivity properties.

Contribution

It introduces a weighted bipartite model for random intersection graphs and characterizes degree distributions based on vertex weights and their distributions.

Findings

Degree of a vertex depends on its weight and the weight distribution of the other vertex type.

Provides analytical expressions for degree distributions in weighted intersection graphs.

Shows how weight distributions influence graph connectivity and degree variability.

Abstract

We study a variant of the standard random intersection graph model ($G(n,m,F,H)$) in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the distributions of these weights, the degree of a vertex is shown to depend on the weight of that particular vertex and on the distribution of the weights of the other vertex type.