The Geometric Block Model and Applications

This is a note accompanying an invited talk at the Allerton conference where we summarize our results related to geometric block model (GBM), a random graph model for communities in networks that is based on geometric graphs. The GBM is distinguished from many other community models because of correlated edge formation, which makes GBM less random in nature, but more complicated to analyze. On the algorithmic side, we describe a simple triangle-counting process that performs sequential edge removal from the graph to reveal the communities. The algorithm critically uses the connectivity properties of annulus graphs or vertex-random graphs.