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Network-valued time series are currently a common form of network data.However, the study of the aggregate behavior of network sequences generatedfrom network-valued stochastic processes is relatively rare. Most of theexisting research focuses on the simple setup where the networks areindependent (or conditionally independent) across time, and all edges areupdated synchronously at each time step. In this paper, we study theconcentration properties of the aggregated adjacency matrix and thecorresponding Laplacian matrix associated with network sequences generated fromlazy network-valued stochastic processes, where edges update asynchronously,and each edge follows a lazy stochastic process for its updates independent ofthe other edges. We demonstrate the usefulness of these concentration resultsin proving consistency of standard estimators in community estimation andchangepoint estimation problems. We also conduct a simulation study todemonstrate the effect of the laziness parameter, which controls the extent oftemporal correlation, on the accuracy of community and changepoint estimation.

Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis