  Community detection, which focuses on clustering nodes or detecting
communities in (mostly) a single network, is a problem of considerable
practical interest and has received a great deal of attention in the research
community. While being able to cluster within a network is important, there are
emerging needs to be able to cluster multiple networks. This is largely
motivated by the routine collection of network data that are generated from
potentially different populations. These networks may or may not have node
correspondence. When node correspondence is present, we cluster networks by
summarizing a network by its graphon estimate, whereas when node correspondence
is not present, we propose a novel solution for clustering such networks by
associating a computationally feasible feature vector to each network based on
trace of powers of the adjacency matrix. We illustrate our methods using both
simulated and real data sets, and theoretical justifications are provided in
terms of consistency.
