Random intersection graphs with tunable degree distribution and clustering

TL;DR

This paper introduces a flexible random intersection graph model where vertex weights influence degree and clustering, enabling the generation of graphs with customizable degree distributions and clustering properties.

Contribution

The paper develops a new model linking vertex weights to degree and clustering, allowing tunable properties including power-law degree distributions.

Findings

Degree distribution depends on vertex weights.

Power law weights lead to power law degree distributions.

Asymptotic clustering expression derived.

Abstract

A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in which each vertex is given a random weight, and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is characterized and is shown to depend on the weight of the vertex. In particular, if the weight distribution is a power law, the degree distribution will be so as well. Furthermore, an asymptotic expression for the clustering in the graph is derived. By tuning the parameters of the model, it is possible to generate a graph with arbitrary clustering, expected degree and -- in the power law case -- tail exponent.