The Research Of Epidemic Spreading And Community Detection Based On Complex Networks

Complex networks have penetrated into many fields such as mathematical subject, bion-omy, engineering and so on. Now the research on complex networks has become a very challenging subject. With the rapid development of computer technology and the wide application of network, higher demand for the research on complex networks has been proposed. At present, great progress has been obtained in network topological structure and modeling, epidemic spreading, community structure, network searching, synchronization and so on. Also there are still many problems in these fields. In this thesis, we study the following three subjects in detail: first, modeling in weighted network; second, epidemic spreading in scale-free network; third, community analysis and search in complex networks structure.The primary contributions of this thesis are listed as follows.Firstly, we further explore the mechanism of complex weighted networks and propose a new model, which incorporates the network topology and the weight dynamics. The new model can capture the essence of the weight dynamics induced by the addition of new nodes with new links and the addition of new links between old nodes, as well as the deletion of some old links.Secondly, we analyze the influence of the epidemic spreading on the nodes with different resistance against epidemic in the scale-free networks and propose a new model to depict this phenomenon.Thirdly, we propose a new algorithm based on local information to detect communities in complex networks. This algorithm can not only extract a proper community for any given nodes, but can also analyze the whole community structure of complex networks.Finally, we further extend our algorithm proposed above. The improved algorithm can get the similar results when analyzing complex networks, but its running time cost is cut down significantly. The time cost of this algorithm is approximately linearly increasing with the size of networks, so this algorithm can be applied to analyze community structure in large networks.