Research On The Centralization Of Complex Networks

The theory of centralization is not a strange name in the statistics, it is the most commonly used tool in the statistical analysis. When it is used in the complex networks, the content becomes bran-new. In these networks represented by huge size and complex structure, the research of centralization is related to how to search out the central nodes. It is different with searching out the geometrical centers and sample means. In the view of complex networks abstracted by sets of nodes and pairs of links, the research on the centralization is provided with its theoretical and practical values.In this paper, by studying the centralization of complex networks, analytical focuses are on the centrality indices of networks, centrality research in the practical networks, centrality research in the topology structures, the relation of centralization and efficiency and the relation of centralization and vulnerability attacking. The main research works are as follows:1) We summarize the development of centralization in the research of complex networks, including the processes of finding the centrality indices. Especially, we introduce several important indices and compare them by putting them in some different models. Consequently, we point out the situations for using them based on network flow.2) We put three centrality indices such as degree centrality, closeness centrality and betweenness centrality into the research of four topology structures of complex networks including the regulation networks, the random networks, the small-world networks and the scale-free networks. Using these indices to measure every network, we get their results of centralization and validate it by analyzing Internet.3) Efficiency index is introduced to evaluate the effect of different indices used in different models. Accordingly, we get the relations of centralization and communication by the efficiency. It would help us to discuss the dynamics problems such as information's congestion, viruses' spreading in complex networks which are brought on discrepancy of centralization.4) Combing with actual model, we analyze the connections of centralization and vulnerability attacking. Thereby the significance of destructing the central nodes in the terrorist networks is revealed.