  Network data are ubiquitous in our daily life, containing rich but often
sensitive information. In this paper, we expand the current static analysis of
privatised networks to a dynamic framework by considering a sequence of
networks with potential change points. We investigate the fundamental limits in
consistently localising change points under both node and edge privacy
constraints, demonstrating interesting phase transition in terms of the
signal-to-noise ratio condition, accompanied by polynomial-time algorithms. The
private signal-to-noise ratio conditions quantify the costs of the privacy for
change point localisation problems and exhibit a different scaling in the
sparsity parameter compared to the non-private counterparts. Our algorithms are
shown to be optimal under the edge LDP constraint up to log factors. Under node
LDP constraint, a gap exists between our upper bound and lower bound and we
leave it as an interesting open problem.
