Moment-based parameter estimation in binomial random intersection graph models

摘要

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