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

Consistent detection and optimal localization of all detectable change points in piecewise stationary arbitrarily sparse network-sequences