Consensus under Network Interruption and Effective Resistance Interdiction

We study the problem of network robustness under consensus dynamics. We first show that maximizing the consensus time subject to removing limited network edges can be cast as an effective resistance interdiction problem. We then show that the effective resistance interdiction problem is strongly NP-hard, even for three types of resistors in the network, hence correcting some claims in the existing literature. Finally, we provide a quadratic program formulation to find a local optimum solution to the consensus interdiction problem.