Study Of Modeling Of Complex Network Topology Based On Degree Distributions

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. In recent years, the research on complex network has been developing rapidly and is extended to many science fields, such as biology, physics and even social science. It boils down to the first reason is with the improvement of computing capability, people can do research in various realistic networks including multimillion nodes which could not be realized in the past, the second reason is they also need to recognize various networks urgently to find out instructional rules. Make use of graph theory, statistical theory and computer simulation etc, this thesis could get the network topology with arbitrary degree distribution. The main contents are outlined as follows:(1) We first introduced the recent progress in the study of complex networks. The basic concepts, such as degree distribution, clustering coefficient, average path length, which characterize the network topologic structure, are defined. Topology models, such as ER model, WS model and BA model are introduced.(2) The degree-rank function is proposed as a statistic characteristic of complex network and the mathematical relationship between degree-rank function and degree distribution is derived. Then the degree-rank function of scale-free network and exponential network is given. Make use of the degree-rank function, the maximum degree and average degree of scale-free network is studied.(3) A method of constructing complex networks with arbitrary degree distributions is proposed. Take scale-free network and exponential network as examples, the efficiency of the method is verified.(4) Topology builder of complex network is designed and the function of topology builder is validated by example.