Research On BA Scale-Free Networks Evolving Models With Random Initializing

Nowadays,the investigating to complex networks attracts increasing number of attention. Complex networks is the important tool the investigating to complex systems. In nature, there are many complex systems, such as the Internet, world wide web, public relation network, citation network of scientific paper, scientific collaboration, exhibit the characteristic of complex networks.Complex networks theory approach is such a result that issue from the observation to relative simple topology structure of networks in different domains. And, recent several years, many research show that many complex systems possess the scale-free topological structures property. Namely, a lot of nodes have only a few connections but abundant connections are possessed by a few nodes. So, to deeply know about complex systems, it is in the extreme essential to study the scale-free networks. It is special necessary to study the scale-free networks since many real systems have the scale-free property.On the basis of the analysis to the evolving mechanisms of the scale-free networks, the evolving networks based on the Barabasi and Albert network evolving model. The node degree distribution is a bank of complex networks, which have been researched deeply. In this dissertation, we use statistical theory approach and optimization approaches to investigate a number of problems in complex networks. The complex networks with power-law degree distribution is a scale-free network, and two essential evolving network mechanisms of the network are the growth and the preferential attachment.The dissertation works a review and broaden research to the Barabasi and Albert evolving network model which is the typical representation of scale-free networks. The exiting typical representation of scale-free networks—the BA model is abstracted from many real systems. But, after some application, it is found the model has more severe defects. So, to make it satisfy topological structures of more real systems.The dissertation works some extending to BA scale-free network model's algorithm. This dissertation provided a kind of scale-free networks model initialized by random, which analyzed degree evolution, degree distribution as well as the range of significant influence to degree distribution by using the continuum theory. Use this model to the Web pages hyperlink in Internet,and analysis of the structure of Web pages, it can contribute to the design of better search engines. The results of computer simulation were in concordance with the theoretical analysis, it is a scale-free networks. The results of numerical simulation show that the new model could reflect some important characters of actual networks well.