International Conference on Information Technology and Computer Science, 3rd (ITCS 2011)
34 Optimal Robustness of Scale-Free Networks
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In this paper, we investigate the connectivity of scale-free networks and introduce degree variance which describes the numerical distance between degree and the average degree of vertices of scale-free networks, and it is looked as a measure on robustness of scale free networks subject to failures. According to degree variance, we investigate the robustness of scale free networks subject to random failures or intentional attacks and discuss the vertices' ability to defense the cascading failures. Furthermore, with the average degree is given, a scheme of nonlinear integer program is designed to defense the random or intentional attacks to scale-free networks according to degree variance. From the scheme, we can obtain the optimal robustness to cascading failures, and the scheme can be adopted to improve robustness of scale-free networks.