Assortativity and clustering of sparse random intersection graphs

TL;DR

This paper analyzes the properties of sparse random intersection graphs, deriving explicit formulas for key network metrics like assortativity and clustering, which remain significant as the network grows large.

Contribution

It provides explicit asymptotic expressions for assortativity, common neighbors, and neighbor degree in sparse random intersection graphs, linking these to degree distributions and model parameters.

Findings

Explicit formulas for assortativity coefficient

Asymptotic expressions for common neighbors

Expected neighbor degree based on degree k

Abstract

We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of adjacent nodes (called the assortativity coefficient), the expected number of common neighbours of adjacent nodes, and the expected degree of a neighbour of a node of a given degree k. These expressions are written in terms of the asymptotic degree distribution and, alternatively, in terms of the parameters defining the underlying random graph model.