Research On Evolution Properties Of Complex Networks Based On Statistical Methods

Complex system and complex networks have become to be the focus of scientific research issue over the 21^st century. Along with more and more researcher involving into complex networks, many significant achievements have been accomplished in various fields. However, which also has brought challenge because of its incomplete theoretical foundation. Whether there exists a normative method for classification? Or have more statistical distribution and properties for characterization of complex structure? How do the dynamics of complex networks affect its topological structure and etc?Based on these several problems mentioned above, this thesis mainly researched on the optimization of nodes and construction in complex networks, evolution mechanism of dynamic networks and its statistical properties. At first, this paper designed a stratified sampling scheme for the common network, which meanwhile maximally maintains its statistical properties. Then the author also used public transfer network of Wuhan city and route network as an empirical study. It shows that this stratified sampling method not only greatly reduces the workload in computation, but also keeps the statistical characters and topological structure in practical application. Considering optimization of complex networks is a dynamic process, this paper researched on the evolution mechanism and statistical properties according to two dynamic evolutions-"rich are richer, poor are poorer" and "life game", simultaneously proved the Markov property of network evolution, and computed the first-step transpose matrix on variation of the node's states and its stationary distribution. Finally, the author studied on the Markov properties of common dynamic complex networks. More over, the author discussed how to determine the posteriori probability distribution of a certain practical network based on the prior information-the connecting probability distribution of edges in stochastic network, scale free network and small world network and the sampling information in practical evolution network. These three statistical methods will provide an excellent reference and platform for the optimization of nodes and structure of static complex networks, the determination of dynamic mechanism in complex networks and also the forecasting and study of invulnerability in complex networks.The innovative points or this thesis are:1) Used stratified sampling method to do sampling design on a practical complex network, of which the theory and thinking have not been analyzed or applied so far in the world. The empirical study shows that this theory and method has not changed its original statistical properties, but greatly reduced the workload and simplifies its computation.2) Researched on the evolution process of complex networks based on Markov process, and also presented a way of computed transpose matrix, stationary distribution and forecasting according to Markov theory. Moreover, on the basic of Bayesian theory, this thesis also originally gave a way for obtaining the posteriori probability function to determine the probability of edges' connection or deletion.