  We consider the offline change point detection and localization problem in
the context of piecewise stationary networks, where the observable is a finite
sequence of networks. We develop algorithms involving some suitably modified
CUSUM statistics based on adaptively trimmed adjacency matrices of the observed
networks for both detection and localization of single or multiple change
points present in the input data. We provide rigorous theoretical analysis and
finite sample estimates evaluating the performance of the proposed methods when
the input (finite sequence of networks) is generated from an inhomogeneous
random graph model, where the change points are characterized by the change in
the mean adjacency matrix. We show that the proposed algorithms can detect
(resp. localize) all change points, where the change in the expected adjacency
matrix is above the minimax detectability (resp. localizability) threshold,
consistently without any a priori assumption about (a) a lower bound for the
sparsity of the underlying networks, (b) an upper bound for the number of
change points, and (c) a lower bound for the separation between successive
change points, provided either the minimum separation between successive pairs
of change points or the average degree of the underlying networks goes to
infinity arbitrarily slowly. We also prove that the above condition is
necessary to have consistency.
