Statistical Inference on Random Graphs: Comparative Power Analyses via Monte Carlo

We present a comparative power analysis, via Monte Carlo, of various graph invariants used as statistics for testing graph homogeneity versus a "chatter" alternative-the existence of a local region of excessive activity. Our results indicate that statistical inference on random graphs, even in a relatively simple setting, can be decidedly non-trivial. We find that none of the graph invariants considered is uniformly most powerful throughout our space of alternatives. Code for reproducing all the simulation results presented in this article is available online.