Matched bipartite block model with covariates

Network analysis has been a very active area of research with applications to social sciences, biology and marketing, to name a few. A fundamental problem in network data analysis is community detection, or clustering: Given a collection of nodes and a similarity matrix among them, interpreted as the adjacency matrix of a (weighted) network, one wants to partition the nodes into clusters, or communities, of high similarity. For undirected networks, a popular model for community-structured networks is the stochastic block model (SBM) [1] and its variants [2, 3], which have been extensively investigated in recent years both in terms of theoretical properties and efficient fitting algorithms. See, for instance [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18] for a sample of the work. On the other hand, a natural structure is often present in many real networks, that of being bipartite, where nodes are divided into two sets, or sides, and only connections between nodes of different sides are allowed.