  We consider the problem of estimating the location of a single change point
in a dynamic stochastic block model. We propose two methods of estimating the
change point, together with the model parameters. The first employs a least
squares criterion function and takes into consideration the full structure of
the stochastic block model and is evaluated at each point in time. Hence, as an
intermediate step, it requires estimating the community structure based on a
clustering algorithm at every time point. The second method comprises of the
following two steps: in the first one, a least squares function is used and
evaluated at each time point, but ignores the community structures and just
considers a random graph generating mechanism exhibiting a change point. Once
the change point is identified, in the second step, all network data before and
after it are used together with a clustering algorithm to obtain the
corresponding community structures and subsequently estimate the generating
stochastic block model parameters. A comparison between these two methods is
illustrated. Further, for both methods under their respective identifiability
and certain additional regularity conditions, we establish rates of convergence
and derive the asymptotic distributions of the change point estimators. The
results are illustrated on synthetic data.
