Robustness of Network Controllability with Respect to Node Removals

Network controllability and its robustness has been widely studied. However, analytical methods to calculate network controllability with respect to node removals are currently lacking. This paper develops methods, based upon generating functions for the in- and out-degree distributions, to approximate the minimum number of driver nodes...

Quantifying the Robustness of Network Controllability

In this paper, we propose closed-form analytic approximations for the minimum number of driver nodes needed to fully control networks, where links are removed according to both random and targeted attacks. Our approximations rely on the concept of critical links. A link is called critical if its removal increases the required number of driver...