The Growing Models Of Complex Networks And The Partitional Method For Community Structure

In recent years, as the WS small-world network model and BA scale-free network model was proposed, the study on complex networks is achieving a climax at home and abroad now. The study on complex network treats the real systems such as the Internet, electricity network and metabolic networks with the viewpoint of systematism. These large-scale networks are widespread in the social system, so people launched a wide research on the topology and the dynamic behavior of networks. In this article, the author investigates the growth model of complex networks with PageRank algorithm, and analyses the community structure of complex networks from the perspective of multivariate statistical analysis. The main production is as follows:1. Proposing a model of networks based on the PageRank algorithm. While considering the preferential attachment mechanism of networks, the classical BA scale-free network model sets the degrees of nodes in networks as the prime factor to decide the probability of the preferential attachment, whereas the affection of other important information of the structure of networks were ignored. And the excellent performance of the Google search engine shows that the PageRank, which is defined in the PageRank algorithm, can describe the importance of the nodes in networks better than the degree. In this article, based on the PageRank algorithm of the Google search engine, we made a new model of growing networks by setting the PageRanks of nodes as the measurement of the probability of preferential attachment, and analyzed its prime characters. The results of numerical simulation show that the new model could reflect some important characters of actual networks well.2. Proposing a new analysis method for the community structure in complex networks. It has great significance in knowing structure of networks and analyzing characteristics of networks that unveiling the community structure in complex networks. The nature of partitioning a network into several communities is that we should extract the major information of the network to the maximal extent. The principle component analysis (PCA) method is just a multi-statistics method which extracts the major information and ignores the less important information at the same time. In this article, based on PCA we proposed a new method of analyzing the community structure in complex networks, and then we analyze the karate club network(Zachary network), the dolphin social network(Lusseau network), and so on, by using this new method. Computational results demonstrate that the proposed method is feasible and effective.