Structural Robustness of Weighted Complex Networks Based on Natural Connectivity
ZHANG Xiao-Ke1, WU Jun1**, TAN Yue-Jin1, DENG Hong-Zhong1, LI Yong 2
1College of Information Systems and Management, National University of Defense Technology, Changsha 410073 2Department of Business Administration, Changsha University, Changsha 410073
Abstract：Natural connectivity has been recently proposed to efficiently characterize the structural robustness of complex networks. The natural connectivity, interpreted as the Helmholtz free energy of a network, can be derived from the graph spectrum. We extend the concept of natural connectivity to weighted complex networks, in which the weight represents the number of multiple edges. We prove that the weighted natural connectivity changes monotonically when the weights are increased or decreased. We investigate the influence of weight on the network robustness within scenarios of weight changing and show that the weighted natural connectivity allows a precise quantitative analysis of the structural robustness for weighted complex networks.
2013, Vol. 30 
