Enhancing Controllability of Complex Networks with Minimum Cost

Complex networks operate in all areas of human life. As a key and popular research direction in the complexity discipline, the study of complex networks has a significant impact and contribution to multidisciplinary fields. In this paper, we study the problem of enhancing network controllability by adding edges from a given candidate set with minimum cost based on the structural controllability theory of complex networks. Specifically, we first formulate such a problem as a bi-objective network optimization model and then transform it into a network flow problem. An algorithm named Controllability Enhancement based Minimum-cost Max-flow (CEMM) is proposed, which can achieve: 1) A certain number of edges selected in the candidate set are added to a network such that the number of driver nodes is minimized; 2) The minimum cost of newly added edges is guaranteed. The feasibility of CEMM is verified by simulations in generative models and real-life networks.