Inference on Edge Density in Undirected Binary Networks

Abstract

Undirected networks are used in a plethora of applications across many disciplines. For example, they are often used to model communication networks, financial networks, transportation networks, protein networks, social networks, and many more. This paper considers binary undirected networks, where the links (or edges) can only take on values of 0 or 1. It is assumed that the edge set of the network is not directly observable and must be estimated via an observable (but noisy) adjacency matrix. The proposed model assumes that changes in the edge set probabilities are due in large part to changes in a one or more exogenous nodal attribute variables. Using a log-likelihood ratio approach, we develop a hypothesis testing framework useful for detecting di↵erences in the edge set probabilities given settings of the nodal attribute variables. Results of the hypothesis test can be used to draw inference on the unknown edge density of the network. We show that the proposed framework is equivalent to logistic regression with a categorical input variable modeled via dummy variables in the logit. Finally, application of the proposed hypothesis testing framework is demonstrated using both a simulated network and an open-source terrorist collaboration network.