Sensitivity of Perron and Fiedler eigenpairs to structural perturbations of a network

One can estimate the change of the Perron and Fiedler values for a connected network when the weight of an edge is perturbed by analyzing relevant entries of the Perron and Fiedler vectors. This is helpful for identifying edges whose weight perturbation causes the largest change in the Perron and Fiedler values. It also is important to investigate the sensitivity of the Perron and Fiedler vectors to perturbations. Applications of the perturbation analysis include the identification of edges that are critical for the structural robustness of the network.