The Research Of Power-Law And Robustness Coupling On The Complex Network Topology

With the development of the complex network research, the safety and reliability of complex networks has become a growing increasingly important issues of concern. Especially in the wide application of Internet, how to provide a safe and reliable network is a common issue for the state and society. The Study shown that "robust and fragile" is an important characteristic of complex networks, the reason is the uneven distribution of network nodes degrees and the power law characteristics. The study of the internal topological structure characteristics of complex network is the basis of improve the reliability of network safety, the inhibition of the complex network failure propagation, improve the network robustness is of great significance. From inside the complex network topology characteristics power-law characteristics research, analyze the network flexibility and robustness, and reduce the failure propagation. The relationship between the power law and robust coupling is the research emphasis in this paper.This paper mainly do the following several aspects:1. Several types of the power-law distribution are analyzed in detail, and make the power law characteristic simulation of BA scale-free network, improved BA networks and the Internet. By analyzing the power-law distribution about degree-rank, frequency-degree and CCDF(d)-degree, compares the degree distribution of Internet, BA scale-free networks, random networks and small world network. Verify that the Internet and BA scale-free network with power law degree distribution characteristics and random network and small world network does not conform to the pow-law. Using MATLAB simulation analysis of the BA network,the improved BA network and Internet topology of power-law index, fitting of BA network power index is 3.0, the improved BA network power index is about 3.23, and level routing Internet power index is about 2.14.2. To study the resilience robustness of the complex network. Introduced the concept of resiliency about the complex network, and points out the resiliency is the ability of the complex network make it quickly return to normal operation after attack. For network dynamics when it is attacked,put forward the mathematical model of network resilience, thereby strengthen network resiliency and reduce the spread of cascading failures. When the network is under attack, using set up network redundancy to increase the load on the node and enhance the network resiliency ability. Based on network more resilience model of situation awareness, perception of threat and influence that exist in the current environment, forecast the potential faults in the network environment, and enhance the resiliency of the network.3. Analysis and comparison of robustness about BA network, improved BA network and the Internet in the event of attack, and make a simulation. Experimental results show that for the BA network, improved BA network and Internet, they have good robustness when encounter random attack. When faced with deliberate attack three networks are vulnerable. By contrast, the Internet is the most vulnerable under deliberate attack, the improved BA network is the most robust. In the case of high load the three networks are more fragile and more easily destroyed, while in the case of the high redundancy, three network robustness are improved. Experimental data show that, whatever in a random attack or determine attack, the improved BA networks have the most robust performance and Internet is the most vulnerable. We may draw a general rule, if the network have a power law characteristics, the greater the power index is stronger robustness.