  We consider an approach for community detection in time-varying networks. At
its core, this approach maintains a small sketch graph to capture the essential
community structure found in each snapshot of the full network. We demonstrate
how the sketch can be used to explicitly identify six key community events
which typically occur during network evolution: growth, shrinkage, merging,
splitting, birth and death. Based on these detection techniques, we formulate a
community detection algorithm which can process a network concurrently
exhibiting all processes. One advantage afforded by the sketch-based algorithm
is the efficient handling of large networks. Whereas detecting events in the
full graph may be computationally expensive, the small size of the sketch
allows changes to be quickly assessed. A second advantage occurs in networks
containing clusters of disproportionate size. The sketch is constructed such
that there is equal representation of each cluster, thus reducing the
possibility that the small clusters are lost in the estimate. We present a new
standardized benchmark based on the stochastic block model which models the
addition and deletion of nodes, as well as the birth and death of communities.
When coupled with existing benchmarks, this new benchmark provides a
comprehensive suite of tests encompassing all six community events. We provide
analysis and a set of numerical results demonstrating the advantages of our
approach both in run time and in the handling of small clusters.
