Exploiting the Robustness on Power-Law Networks

Many complex networks are discovered to follow the powerlaw distribution in degree sequence, ranging from the Internet, WWW to social networks. Unfortunately, there exist a great number of threats to these complex systems. In this context, it is crucial to understand the behaviors of power-law networks under various threats. Although power-law networks have been found robust under random failures but vulnerable to intentional attacks by experimental observations, it remains hard to theoretically assess their robustness so as to design a more stable complex network. In this paper, we assess the vulnerability of power-law networks with respect to their global pairwise connectivity, i.e. the number of connected node-pairs, where a pair of nodes are connected when there is a functional path between them. According to our in-depth probabilistic analysis under the theory of random power-law graph model, our results illustrate the best range of exponential factors in which the power-law networks are almost surely unaffected by any random failures and less likely to be destructed under adversarial attacks.