Moment-based parameter estimation in binomial random intersection graph models

TL;DR

This paper introduces moment-based estimators for key parameters in binomial random intersection graph models, demonstrating their consistency and showing the empirical transitivity aligns with the theoretical clustering coefficient.

Contribution

It proposes a novel method for estimating model parameters from a single observed graph, with proven consistency under certain sampling conditions.

Findings

Estimators are consistent when the sample size is large enough.

Empirical transitivity closely matches the theoretical clustering coefficient.

The method applies to large, sparse networks.

Abstract

Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected. This paper discusses the estimation of these parameters from a single observed instance of the graph, using moment estimators based on observed degrees and frequencies of 2-stars and triangles. The observed data set is assumed to be a subgraph induced by a set of $n_0$ nodes sampled from the full set of $n$ nodes. We prove the consistency of the proposed estimators by showing that the relative estimation error is small with high probability for $n_0 \gg n^{2/3} \gg 1$. As a byproduct, our analysis confirms that the empirical transitivity coefficient of the graph is with high probability close to the theoretical clustering coefficient of the model.