Local Natural Connectivity in Complex Networks

In network theory,a complex network represents a system whose evolving structure and dynamic behavior contribute to its robustness.The natural connectivity is recently proposed as a spectral measure to characterize the robustness of complex networks.We decompose the natural connectivity of a network as local natural connectivity of its connected components and quantify their contributions to the network robustness.In addition,we compare the natural connectivity of a network with that of an induced subgraph of it based on interlacing theorems.As an application,we derive an inequality for eigenvalues of Erdös-Rényi random graphs.