Hurdle Blockmodels for Sparse Network Modeling

A variety of random graph models have been proposed in the literature to model the associations within an interconnected system and to realistically account for various structures and attributes of such systems. In particular, much research has been devoted to modeling the interaction of humans within social networks. However, such networks in real-life tend to be extremely sparse and existing methods do not adequately address this issue. In this article, we propose an extension to ordinary and degree corrected stochastic blockmodels that accounts for a high degree of sparsity. Specifically, we propose hurdle versions of these blockmodels to account for community structure and degree heterogeneity in sparse networks. We use simulation to ensure parameter estimation is consistent and precise, and we propose the use of likelihood ratio-type tests for model selection. We illustrate the necessity for hurdle blockmodels with a small research collaboration network as well as the infamous Enron E-mail exchange network. Methods for determining goodness of fit and performing model selection are also proposed. Supplementary materials for this article are available online.