Co-clustering of non-smooth graphons

Theoretical results are becoming known for community detection and clustering of networks; however, these results assume an idealized generative model that is unlikely to hold in many settings. Here we consider exploratory co-clustering of a bipartite network, where the rows and columns of the adjacency matrix are assumed to be samples from an arbitrary population. This is equivalent to assuming that the data is generated from a nonparametric model known as a graphon. We show that co-clusters found by any method can be extended to the row and column populations, or equivalently that the estimated blockmodel approximates a blocked version of the generative graphon, with generalization error bounded by n^{-1/2}. Analogous results are also shown for degree-corrected co-blockmodels and random dot product bipartite graphs, with error rates depending on the dimensionality of the latent variable space.