  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.
