Modeling Analysis Of The Evolution Model Of Scale-free Network With Correlation Degree

The Internet has become the representative of the rapid development of network information technology, the development also marked that human society has entered into the complex network era. In academia, researchers have empirical studied a variety of complex network such as the social network, information network, technology network and biological network, the studies shown that almost all real network has small-world effect, and the node’s degree follows a power-law distribution.Nineties, Barabasi and Albert was first proposed a network model which can generate scale-free properties—BA model, this model proposed theoretical understanding of complex networks has opened a new chapter.In the BA model,based on a variety of improvements or extensions scale-free network model have been proposed by researchers, such as the G growth model, fitness model etc.. In this paper, scale-free network have been studied, the main work is as follows:(1)This paper presents a correlation-based scale-free network model. Based on the new given definition of the correlation,we introduced the correlation βi to the scale-free networks, at each time step, the new node will connected to the m old nodes of the network preferred by correlation degree, and generate m new edges. On the formation of a network’s degree distribution by such evolution, calculated results show that the degree distribution of the correlation degree model follows a power-law distribution, and the range of degree index of the model is extend from [2,3] of BA model to [2+α,3+α],a∈[0,1]. For the correlation degree model, we choose one improved model of BA scale-free network which was mature studied currently—fitness model, and compared them form the simulation of the degree distribution to some relevant parameters of complex networks, multifaceted shows that the correlation degree model is better than the fitness model and the correlation degree model has more realistic network characteristics than the fitness model.(2)With the increasingly developed network information, the attention of public opinion on the university network is also increasingly important. The correlation degree model will be applied to simulated the evolutionary process of a real university forum.By using this model, it not only monitoring public opinion on the university network platform to monitor the sensitive topic of student network user groups for evolutionary analysis, but also on the students often use a variety of media user groups for analysis, and lay a foundation of forecasting public opinion.(3)For the further study of the correlation model theory, the unweighted network was extended to weighted network, presents the scale-free weighted evolving network model based on the correlation degree, and theoretically according to the correlation degree existed fixed value and uncertain vale two cases respectively discusses the intensity distribution and degree distribution of the weighted network,the discusses results show that the weighted network model based on the correlation degree can form a scale-free network.