Target Controllability of Multiplex Networks With Weighted Interlayer Edges

In this work, we focus on the target controllability of multiplex networks with weighted interlayer edges representing the cost for control, which is faced in many real world applications but remains unsolved. The main objective is to locate a minimum number of nodes with external control sources to ensure the controllability of a target subset of the nodes, concurrently guaranteeing the cost for controlling the subset reaches the minimum. To solve this problem, we first convert it into a path cover problem, and then model it as a minimum cost maximum flow problem, which can be solved efficiently using algorithms in graph theory. This method is termed as 'Minimum Cost Maximum Flow based Target Path-cover' (MCMFTP). By using MCMFTP, we have studied the effect of the proportion of target nodes, the number of layers, and the distribution of weights on the controllability of multiplex networks. Simulation results indicate that our approach is an effective tool to study how the multi-layer nature of networks affects target controllability in multiplex networks and would provide theoretical and empirical insights into real applications.