  In this paper we propose methodology for inference of binary-valued 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. Community detection methods such as block modelling
typically require binary-valued adjacency matrices as a starting point. Hence,
a main motivation for the methodology we propose is to obtain binary-valued
adjacency matrices from such pairwise measures of strength of association
between variables. 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 and data-sets.
