复杂网络分形特性的统计分析-计算机系统结构专业论文.docxVIP

哈尔 哈尔滨工业大学理学硕士学位论文 - - II - Abstract At present, the research on complex networks has been expanded to a variety of different fields. Research methods have developed variously. With these methods and powerful computing ability of the computer, the research on complex network has become deeper and deeper. From the research on structure characteristic of the small-world and scale-free network, the basic topological structure of complex networks has been the focus of research. With the in-depth study of complex networks, the self-similar fractal characteristic of complex networks has been excavated. The research on complex networks has come to a new stage. This paper focuses on the research of the fractal characteristic of complex networks. We analyze the origin and the authentication of fractal characteristic of complex networks, apply some weight-adding methods to different network models and compare the results between original networks and weighted networks. Finally, we put forward a complex network topology reconstruction algorithm to adjust the network structures and make them fractal. Firstly, we introduce the basic statistical characteristics of complex networks and several common complex network models. Then, we describe the fractal characteristic and the application of the renormalization group method to complex networks. We construct a new kind of network model with scale-free and fractal characteristics. Secondly, exploring the origin of fractality in complex networks. Here we introduce three box-covering algorithms: compact-box-burning algorithm, greedy coloring algorithm, and MEMB algorithm. We improve the MEMB algorithm and apply it to the complex networks which are weighted with the AdjustCD and WD methods. The results of protein-protein interaction networks and fractal network growth models prove that it is also effective in verifying the existence of fractality in complex networks. Lastly, we select the skeleton of a complex network as the target and