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