Controllability emerging from conditional path reachability in complex networks

Controllability of complex networks is a fundamental requirement to orientate the networks toward a sustainable way of development. Determination of link weights and calculation of eigenvalues of large-scale matrices are two inevitable problems in applying the exact controllability framework in complex networks. Here, we introduce a novel controllability analysis approach based on the controllability index and the reachability matrix to identify the minimum set of driver nodes, in order to achieve complete regulation of arbitrary networks with general configurations. An effective algorithm is theoretically developed via using only the 0–1 binary structure of the network. Theoretical analysis and numerical examples show that our proposed algorithm possesses structural adaptability and control robustness under the weighted perturbation.