Driver-Node based Security Analysis for Network Controllability

In the study of network controllability, because driver nodes are vulnerable to control hijack and removals, and harmfulness of removing a driver node is still unknown. Therefore, to defend against such attacks, we identify each vertex of all minimum sets of driver nodes firstly. Also, to know the harmfulness of removing a driver node, we classify those identified nodes by impacts of removing a driver node on the minimum set of driver nodes to control the residual network. By the minimum input theorem, given a digraph, these two issues are respectively solved by finding each vertex that is an unmatched node related to a maximum matching, and classifying it by the impact of its removal on the number of unmatched nodes of the residual digraph. As a result, our driver-node identification and classification are executed in more efficient polynomial time than related works.