Deng Hong-zhong

Natural Connectivity of Complex Networks

The concept of natural connectivity is reported as a robustness measure of complex networks. 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 natural connectivity with other typical robustness measures within a scenario of edge elimination, it is demonstrated that the natural connectivity has an acute discrimination which agrees with our intuition.

Structural Robustness of Weighted Complex Networks Based on Natural Connectivity

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.

A Robustness Model of Complex Networks with Tunable Attack Information Parameter

We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.

Attack Robustness of Scale-Free Networks Based on Grey Information

We introduce an attack robustness model of scale-free networks based on grey information, which means that one can obtain the information of all nodes, but the attack information may be imprecise. The known random failure and the intentional attack are two extreme cases of our investigation. Using the generating function method, we derive the analytical value of the critical removal fraction of nodes for the disintegration of networks, which agree with the simulation results well. We also investigate the effect of grey information on the attack robustness of scale-free networks and find that decreasing the precision of attack information can remarkably enhance the attack robustness of scale-free networks.

Normalized entropy of rank distribution: a novel measure of heterogeneity of complex networks

Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution (NERD) is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.