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Evolving complex networks are abundant in the real world, i.e., Networks with different sizes (number of nodes) may originate from the same evolving system. In this paper, we use some typical evolving models of complex networks to evaluate the performances of graph spectra. The experimental results verify that the normalized Laplacian spectrum is a good indicator to distinguish between different evolving...
We introduce the concept of natural connectivity as a measure of structural robustness in complex networks. The natural connectivity characterizes the redundancy of alternative routes in a network by quantifying the weighted number of closed walks of all lengths. This definition leads to a simple mathematical formulation that links the natural connectivity to the spectrum of a network. The natural...
The natural connectivity as a novel robustness measure of complex networks is proposed. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It is shown that the natural connectivity can be derived mathematically from the graph spectrum as an average eigenvalue and that it changes strictly monotonically with the addition or deletion of edges. By comparing the...
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