Network inference and community detection, based on covariance matrices, correlations and test statistics from arbitrary distributions

Abstract

In this paper we propose methodology for inference of binary adjacency matrices from various measures of the strength of association between pairs of network nodes, or more generally pairs of variables. This strength of association can be quantified by sample covariance and correlation matrices, and more generally by test-statistics and hypothesis test p-values from arbitrary distributions. Binary adjacency matrices inferred in this way are then ideal for community detection, for example by block-modelling. The proposed methodology is applicable to large high-dimensional data-sets and is based on computationally efficient algorithms: we illustrate its utility in a range of contexts including biological and social/communication networks.