The Topological Structure, Avalanche Characteristic And Dynamics Of Complex Networks

This dissertation is concerned with the basic concept of complex network and the study of the topological properties of the airport network of American (ANA);with five important complex network models and we propose a model growing by preferential copying mechanism based on the observation of biological network;with the self-organize critical (SOC) in nature and the SOC in the generalized small-world networks (SWN). So, this thesis can be divided into three parts.The first part introduce some basic concepts and properties of complex network, after that, we study the topological properties of ANA as an example, which is a weighted directed network. The airport network of American is a small world network: it has large average clustering coefficient (0.618) and small average path length (2.4), different from most of the SWN, it is a hierarchical network (P(k) ∝ k^-a)), its disassortative coefficient r is -0.37, just like most of the biological and technical networks. Comparing with other airport networks, such as airport network of WWW (ANW), China (ANC). India(ANI), we conclude that the airport networks are all small world networks and more constrained by the geographical condition.The second part introduce some important network models, as Erdos-Renyi graph, Watts-Stragatz model, Barabasi-Albert model. These models are all well fit some areas' observation. So far, different from social and technical network, biological network is paying much more attention than others, for there are so much abundance phenomena in the biological networks. We propose a growing network by preferential copying (GNPC) model, it can reproduce most of the biology phenomena, such as scale-free degree distribution ((P(k) ∝ k^-Td)), the property of small world and hierarchical.Finally, we introduce the concept of self-organize critical, two SOC models and some SOC work done in the complex networks. We study the sandpile in the generalized small world network (GSWN) and get interesting result. As decreasing the shortcut in the GSWN which means smaller average degree, the dimension of avalanche in spatial and time will increase, more importantly, the dimension in time always larger than that of the time. These results are more analogy to the diffusion-limited aggregation (DLA) in the generalized small world network.