Topology And Dynamics Behaviour Of Scale-free Networks

One of the most important findings of the complex network is the scale freeproperty. Impirical studyings show that most of the real networks are scale-freenetworks. The scale-free networks have the special error tolerant and dynamical be-havior because of its special topology. In this paper we study the structural propertyand dynamics behavior of scale-free networks.1. We propose a disassortative weighted network model. In the model, each newnode is connected to some old nodes. Meanwhile, old nodes are connected possibly toeach other. By Mean-Field approach and numerical simulation, we show the degree,strength and weight distributions all have power-law tail. In particularly, the modelproduces a disassortative network.2. We study the optimal strategy of four attacks on scale-free networks. Theseattacks with the removal of edges are performed by the random and intentionalattacks, the maximum degree-based and edge-based attacks. The property of thenetworks is measured by the global efficiency E, the values of E are calculatedunder some given p (the probability of removing a edge) and f (the fraction ofnodes attacked). By the simulations and analysis of the data, we obtain the optimalstrategies for four different attacks, respectively.3. We propose a SIR model with identical infected ability. Through restrictingthe edges' infccted ability of susceptiblc nodes, we conclude that in heterogencousuncorrelated networks, there is an fixed effective spreading rate thresholdλ_c=1/A.