  Since network data commonly consists of observations on a single large
network, researchers often partition the network into clusters in order to
apply cluster-robust inference methods. All existing such methods require
clusters to be asymptotically independent. We prove that for this requirement
to hold, under certain conditions, it is necessary and sufficient for clusters
to have low conductance, the ratio of edge boundary size to volume, which
yields a measure of cluster quality. We show in simulations that, for important
classes of networks lacking low-conductance clusters, cluster-robust methods
can exhibit substantial size distortion, whereas for networks with such
clusters, they outperform HAC estimators. To assess the existence of
low-conductance clusters and construct them, we draw on results in spectral
graph theory showing a close connection between conductance and the spectrum of
the graph Laplacian. Based on these results, we propose to use the spectrum to
compute the number of low-conductance clusters and spectral clustering to
compute the clusters. We illustrate our results and proposed methods in
simulations and empirical applications.
