Identification of influencers in networks with dynamic behaviors

Identification of vital or vulnerable components of networks with dynamical process is essential for information mining and security management. Centrality indexes proposed from the perspective of structural connectivity are not applicable to identify influencers in the process of network dynamical dissemination and evolution frequently. With a broad range of steady-state dynamical processes including biochemical dynamics (B), epidemic processes (E), birth–death processes (BD) and regulatory dynamics (R), we propose S-index from the correlation matrix describing the system’s response under perturbation, which can quantify both the dynamical propagation range and influence extent of network node. Simulation and comparison results show that both the dynamical process and disturbance intensity at an individual node affect the value of S-index, our index can recognize the potential critical nodes, which are the nodes that appear to be unimportant in structure but do play a vital role in spreading dynamics. Then we explain how to obtain the S-index through the propagation process and give a rough estimation of the propagation radius by the degree of the disturbed node. What we study actually creates a richer way of exploring the network control and optimization.