Network Cluster?Robust Inference

Since network data commonly consists of observations from a single large network, researchers often partition the into clusters in order to apply cluster?robust inference methods. Existing such methods require be asymptotically independent. Under mild conditions, we prove that, for this requirement hold network?dependent data, it is necessary and sufficient that have low conductance, ratio edge boundary size volume. This yields simple measure cluster quality. We find simulations when control better than HAC estimators. However, important classes networks lacking low?conductance clusters, former can exhibit substantial distortion. To determine number construct them, draw on results spectral graph theory connect conductance spectrum Laplacian. Based these results, propose use clustering them.