Study On Complex Networks And SMS Networks

Complex network is one of the most effective tool to real systems, such as, urban transportatio systems, communication systems and so on. Recently, on purpose of having a better understanding of complex systems to solve the complicated problems of real life, the research of complex networks have become one of the most hot area. In the study of complex networks, the topology of complex networks is the most important form of reflecting the features and function of complex networks. In order to explore the behavior and function of real networks, we make a study of complex networks from multiple angles. We attempt to have deep analyses to the network models and the human dynamic behavior of complex networks. The main results are as follows:1,The development and research of complex networks were reviewed briefly. The research contents, such as, the evolving network models and generative mechanism of complex networks, the structure and properties of complex networks, the dynamics of complex networks and so on were introduced in detail. In addition, the unsettled problems were also listed. See Chapter 1.2,We make a general summary of the definition of some statistical parameters in complex networks, the degree distribution, the degree correlation, the clustering coefficient and the average path length. We also summarize the key models of complex networks, which are the random graph model, the small-world network model and the scale-free network model. Then, we have a description of several methods for solving degree distribution, the way of solving degree correlations and the shortest path length. See Chapter 2.3,On the basis of pre-existing network models, we propose a few of new models, which includes the modified extended BA model and the group preferential model. These models are more close to real networks, and they can fit the features of real systems well. What's more, the group preferential model provides a realization of the preferential attachment rule of the BA model. As to these models, we give rigorous analyses to the topology parameters from the perspect of probability. We not only derive the degree distribution of the models, but also analyze the degree correlations. The simulation analysis indicates that the theoretical results agree well with the simulation results. See Chapter 3.4x Based on the short message communication data, the short message service network is in-depth analyzed. Firstly, empirical studies are given with regard to the short message communication data, the distribution of time intervals between two short messages'sending of single users and all users are also provided. Secondly, as to the short message service networks, we give a research on unweighted and weighted short message networks. The relationship between the degree and the added time of the vertices is discussed. The degree distribution is considered as well. At the mean time, the relationship between the time and the average degree of network is also studied. Moreover, we provide a weighted short message service network model, which is more fitted to the real short message service networks. Through the change of each different parameter, diverse forms of degree distributions are obtained. At last, we not only take the distribution of time intervals of each user's short message sending into consideration, but also studied the distribution of time intervals between two given users'short message sending. See Chapter 4.5-. We have a summary on the thesis, and look into the prospect of future research work. See Chapter 5.