| Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. Centrality measures describe a node's importance by its position in a network. Here we consider dynamical influence as a centrality measure based on the leading eigenvector of the coupling matrix of the system. It measures explicitly to which extent a node's dynamical state affects long-term collective behaviour. For critical spreading, e.g. in the SIR/SIS models and the Ising model, dynamical influence ranks nodes by their capability of spreading an epidemic or damage. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single node. |
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