Mining maximum matchings of controllability of directed networks based on in-degree priority

Usually, according to matching theory, we seek a maximum matching in complex networks and control those unmatched nodes for complex networks achieving a desired state. Here, an algorithm is proposed to obtain maximum matchings of directed complex networks. This algorithm to find maximum matching enables effectively eliminating the transformation process of its bipartite equivalent graphs. This algorithm, which is used to mine maximum matchings in many real complex networks, is efficiently. Simulation results show that the number of driver nodes is determined basically by the average degrees of networks and the degree distribution of networks.