Spectral Measure of Structural Robustness in Complex Networks

Authors:
Jun Wu;Mauricio Barahona;Yue-Jin Tan;Hong-Zhong Deng
Affiliations:
College of Information Systems and Management, National University of Defense Technology, Changsha, China;Department of Bioengineering, Imperial College London, London, U.K.;College of Information Systems and Management, National University of Defense Technology, Changsha, China;College of Information Systems and Management, National University of Defense Technology, Changsha, China
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Year:
2011

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Abstract

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 connectivity can be regarded as an average eigenvalue that changes strictly monotonically with the addition or deletion of edges. We calculate both analytically and numerically the natural connectivity of three typical networks: regular ring lattices, random graphs, and random scale-free networks. We also compare the proposed natural connectivity to other structural robustness measures within a scenario of edge elimination and demonstrate that the natural connectivity provides sensitive discrimination of structural robustness that agrees with our intuition.