Network cross-validation by edge sampling

Statistical methods for network data have received a lot of attention because of the wideranging applications of network analysis. There is now a large body of work on methods and models for networks, including the stochastic block model (SBM) [Holland et al., 1983], the degree-corrected stochastic block model (DCSBM) [Karrer and Newman, 2011], and the latent space model [Hoff et al., 2002], to name a few. While this gives the practitioner plenty of choices, there is a lot less work on the crucial question of how to select the best model for the data, as well as how to choose tuning parameters for the selected model, which is often necessary in order to fit it. In some specific problems, progress has been made recently, for instance, in the much-studied problem of community detection. Community detection is the problem of clustering network nodes into groups, and most of the methods proposed over the last twenty years or so require the number of communities K as input.