## Moment-based parameter estimation in binomial random intersection graph models

*Proc. 14th Workshop on Algorithms and Models for the Web Graph (WAW), 2017*.- Lecture Notes in Computer Science 10519, pp. 1–15, Springer 2017
- doi:10.1007/978-3-319-67810-8_1
- arXiv:1704.04278

### 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*. 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.

_{0}≫ n^{2/3}≫ 1