Topological and Spectral Perturbations in Complex Networks

Recently many network perturbation techniques, mainly involving topological and spectral perturbations, have been employed to analyze and improve the robustness of complex networks. However, to the best of our knowledge, the relationship between topological perturbation and spectral perturbation has not been studied intensively so far. We introduce a new robustness measure, subgraph centrality defined by eigenvalue spectrum, to investigate the impact of topological perturbation on eigenvalue spectrum. A specific definition of spectral perturbation is given, such that we can examine the impact of spectral perturbation on topological property by a measure of topological performance: global efficiency. Our main finding is that the spectral perturbations we define are equivalent to the conventional topological perturbations, especially for scale-free networks