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Sun, P. (author), Kooij, Robert (author), Van Mieghem, P.F.A. (author)In this paper, we propose closed-form analytic approximations for the number of controllable nodes in sparse communication networks from the aspect of network controllability, considering link-based random attack, targeted attack, as well as random attack under the protection of critical links. We compare our approximations with simulation...journal article 2021