Reachability-Based Robustness of Controllability in Sparse Communication Networks

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 results on communication networks. Results show that our approximations perform well for all three attack strategies as long as the fraction of removed links is small. Only when the fraction of removed links is large, our approximation for targeted attacks does not fit well with simulation results. Finally, we validate our approximations using 200 communication networks and some synthetic networks. Results show that our approximations perform well in most cases.