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Perturbation results for the Estrada index in weighted networks

The logarithm of the Estrada index has been proposed recently as a spectral measure to character efficiently the robustness of complex networks. In this paper, we explore the Estrada index in weighted networks and develop various perturbation results based on spectral graph theory. It is shown that the robustness of a network may be enhanced even when some edge weights are reduced. This is of particular theoretical and practical significance to network design and optimization.