Topology,Dynamical Behavior And Their Empirical Study On Complex Network

Complex networks has set off a renaissance home and abroad in recent years. Science and engineering researchers from different areas are all have strong concern to it. Complex networks can be used not only to describe the skeleton of various networks such as technology, biology and complicated social system, but also a powerful tool of studying their topological structure and dynamic behaviors. Researchers focus on the general characteristics of the actual network which have huge nodes and complicated connecting structure, particularly the relationship between network topology and its function, its network dynamics behavior, its formation mechanism of the structure and function and its evolution, ect.This thesis selected three typical nonlinear complex networks from actual networks: airline network, electrical circuit network, the science paper for download network. We carried out in-depth research on the universal application and particularity of complex network, combined with graph theory and topology, nonlinear science, modem statistics physics and network design principles of engineering technology. We discussed the connection of the network's structure and its function, such as the relation between network topology and network the fault tolerance capability. We analyzed the complex behaviors which displayed according to the changes of the network's topology and dynamic characteristics during the dynamic evolution period. The research on dynamic characteristics of complex network can help us not only to have better understanding and explanation of the complex dynamics phenomenon which the real network showed, but also the fotmdation of a truer reflection network model. We can make the network theory for our own use to design networks that have good performance.The main points and innovations in this thesis are the following:1. We chose one network affiliated with a specific airline company (Austrian Airlines) as a typical representative of directed weighted network. We had comprehensive and detailed analysis of its small world characteristic and scale-free feature, simulated and calculated the important statistical features of weighted network. Based on the real-time data of one-week flights, we had in-depth study on the mechanism and evolution model of airline network's nodes and its weights. We discussed the dynamics of the network and its evolution which provided the necessary basis to amend the assumption of the BBV model in order to closer to the real system. On the foundation of above mentioned work, we discovered the distinctive statistical complex behavior of this airline network: (1) The degree-degree correlation of Austria's airline showed that no matter how the k value was, it displayed the negative correlation matching characteristic obviously, that is to say, these key airports tended to link with the smaller airports. (2)The cluster-degree correlation indicated that in k＜7 circumstances, Austria airline network had no clear hierarchy. Only k≥7, it had hierarchical structure. Such a network topology mechanism which had layered topology with ER random model and BA scale-free model could not be explained as they do not contain mechanisms conducive to the emergence of modules. Therefore, our empirical results is a useful effort not only for reappear the hierarchy but also for the new network evolution model which considered the geometrical effect.2. An effective design of electrical circuit network depends on whether there are different short connections between the component groups to a large extent. Therefore, the circuit network is closer to the WS model compare to other real systems. Our research is the first one in China that applied the complex network theory to analyze a system-level wireless receiver circuit network. We discussed the topology of circuit network and the function of its components. At the same time, we simulated and calculated the probability distribution function curves of components. What's more, we analyzed the statistical properties of network's connecting degrees distribution, confirmed that it is an index power law with cut-off which unlike typical BA scale-free network model. Then, we analyzed the possible reasons that caused this network evolution. We need to use different short-range connectivity and integrated circuits in integrating all modules, that is to say, to achieve the optimization of physical design, to use the least circuit components and to simplify connection. In addition, we simulated and calculated the changes of topology when the circuit network faced the random failures and deliberate attacks by using percolation theory in Statistical physics and strategies in network attack, do the further analysis of the relationship among the dynamic behavior, the robustness and the fragility. According to the above, we provide theoretical guidance to optimal circuit design.3. We treated the science paper for download network as a prototype of evolution networks which is an innovative attempt, focused on its dynamics and evolution mechanisms. It supported the study of the entire information network's structure. Three different angles were used in the frequency distribution of articles download network whether it had power-law and scale-free phenomena, those were Zipf's Law, Pareto's power-law distribution Law and Tsallis entropy theory. The thought never appeared in the area of complex network research. After we published the results of research on this area, many other scholars made reference. Then, we also considered the complex dynamic behavior of download network showed by nodes traffic in a three-year period, and analyzed the fluctuation scale phenomena that is commonly found in both Macroscopic World and Micro World. We discussed the universal classification (that is,α= 1 / 2 andα= 1), found that the average download rate the grading variance were in the rapid exponential decay while the variance the grading variance had no obvious relations. The varianceσof the download rate distribution met with the average flow^{＜f＞} of power-law standards, that is,σ∝＜f＞^α. Scale parameter changed with the time window, from 0.60 to 0.89. We explained the formation of fluctuation mechanism by using Barabasi and Menezes' external driving model and a simple flow model.