Model Selection for Degree-corrected Block Models

Understand

The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables.

• Together, these issues mean that the usual model-selection criteria do not work properly for networks.
• We illustrate these challenges, and show one way to resolve them, by considering the key network-analysis problem of dividing a graph into communities or blocks of nodes with homogeneous patterns of links to the rest of the network.
• The standard tool for doing this is the stochastic block model, under which the probability of a link between two nodes is a function solely of the blocks to which they belong.