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We provide a theoretical analysis of node importance from the perspective of dynamical processes on networks.In particular,using Markov chain analysis of the susceptible-infected-susceptible (SIS) epidemic model on networks,we derive the node importance in terms of dynamical behaviors on network in a theoretical way.It is found that this quantity happens to be the eigenvector centrality under some conditions,which bridges the topological centrality measure of the nodes with the dynamical influence of the nodes for the dynamical process.We furthermore discuss the condition under which the eigenvector centrality is valid for dynamical phenomena on networks.