Structural Controllability of Multiplex Networks with the Minimum Number of Driver Nodes

In this paper, we focus on the problem of structural controllability of multiplex networks. By proposing a graph-theoretic framework, we address the problem of identifying the minimum set of driver nodes to ensure the structural controllability of multiplex networks, where the driver nodes can only be located in a single layer. We rigorously prove that the problem is essentially a minimum-cost flow problem and devise an algorithm termed "Minimum-cost Flow based Driver-node Identification" (MFDI) which can achieve the optimal solution with polynomial time complexity. Extensive simulations on synthetic and real-life multiplex networks demonstrate the validity and efficiency of the proposed algorithm.