Parameter estimators of random intersection graphs with thinned communities

TL;DR

This paper introduces a flexible statistical network model based on random intersection graphs with thinned communities, allowing for tunable network properties and consistent parameter estimation in large, sparse networks.

Contribution

It develops a new, analytically tractable model with a parameter q for controlling network features and provides methods for consistent parameter estimation.

Findings

Model captures tunable density, transitivity, and degree fluctuations.

Parameters can be consistently estimated using moment estimators.

Applicable in large, sparse network regimes.

Abstract

This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability $q$ via the community. In the special case with $q=1$ the model reduces to a random intersection graph which is known to generate high levels of transitivity also in the sparse context. The parameter $q$ adds a degree of freedom and leads to a parsimonious and analytically tractable network model with tunable density, transitivity, and degree fluctuations. We prove that the parameters of this model can be consistently estimated in the large and sparse limiting regime using moment estimators based on partially observed densities of links, 2-stars, and triangles.