Constrained Maximal Controllability of Complex Networks

This article focuses on the constrained maximal controllability of complex networks, which aims to maximize the generic dimension of controllable subspace of networks with a given candidate set of constrained input locations. To address this issue, we first transform it to a maximum general-cactus cover problem. By introducing network flow, this problem is further converted to a minimum-cost maximum-flow problem. An algorithm named minimum-cost maximum-flow-based general-cactus cover (MMGC) is proposed to achieve the optimal solution. Furthermore, a series of simulations on Erdős-Rényi networks (ERNs) and scale-free networks (SFNs) and applications in network controllability robustness demonstrates the effectiveness of MMGC. The simulation results have revealed that augmenting the number or range of inputs can enhance the controllability of networks, and the presence of multicyclic structures significantly strengthens the controllability robustness of complex networks.