Complex Network Statistical Description And Nature Of The Study

Complex networks describe a wide variety of high technological systems. For example, the network of chemical reactions, Internet network, social network, the World Wide Web and so on. The aim of the studies on these networks is to investigate their mechanisms, understand their developing rules, and find the relationship between their structure and the complex functioning processes on them, so as to accumulate the knowledge about the natural disciplinarians dominating the complex systems. This thesis reports some realizations in our complex network's research. The first chapter is an introduction part, and most of our works are described in chapters 2 to 6.The second chapter suggests a self-adaptive bi-particle graph model, which describes the collaboration network between film actors or the principal investigators and their assistants. The model considers the choices, strategies, competitions, and the induced evolutions of the scientists or film actors and as well as the evolution of the whole network. The simulation results of all the different single-particle graphs obtained by different methods of projection show a good agreement with the statistical data. That shows a self-adaptive complex network can self-organize to a small world and scale-free structure. This article also discusses the similarities and differences of the simulation results of the different projected single-particle graphs of the bi-particle graph.The third chapter reports the properties of Chinese power grid those we have statistically observed. The properties show a good agreement with the universal ones. We also present a dynamical model, which may reproduce the developing process of Chinese power grid in the coarseness. This very simplified description idea for the power grid may give a kind of elicitation to the scientists who study the models of power grid.The forth chapter reports some statistical properties of river network of Yangtze as well as the statistical properties of shipping and commerce between the ports along theriver. In the chapter we also suggest a complex self-adaptive model that describe the shipping and commerce network. A computer simulation on the development mechanism and commercial competitions of the ports has been performed. The simulation results are compared with the statistical data.In the fifth chapter we define a new parameter, the successful collaboration ration (Cr). It is our wish that the parameter can connect the structure of complex networks and their working characteristics. We report the distribution rules of Cr parameter in the collaboration network between film actors or the principal investigators and their assistants. Also, the relationship between structure of a simplified complex network model and the interesting working properties, the tolerance and sensitivity, has been reported. The model is constructed for a study on the avalanches in the power grids.The last chapter presents, from a view of point, a discussion on the development history of the models of epidemic spreading. We suggest that it can be divided into three stages: deterministic models, cellular automata models, and complex network models. We briefly introduce some samples of the simulation on the process of SARS spreading in Beijing by means of deterministic models, cellular automata models, and complex network models, respectively, conducted by our group or other groups, so as to show that all the achievements in the three stages are helpful for establishing models, performing forecasting and searching for rules of SARS spreading, but different models have different characteristics. In the introduction of the simulation with complex network models we emphasize the important achievements in the recent studies, which are the influences of the small world characteristic, the scaling-free characteristic and the high-clustering characteristic of the network on the epidemic spreading. We also report the results obtained by our group in the simulation of SARS spreading those correspond to the achievements.