Study On Method Of Dynamic Network Structure Entropy Measurement Based On BA Model

The existence of a large number of complex networks in reality promote the development of the research on complex networks. Network structure reflects the relationship between different nodes in complex networks. Whether network structure is reasonable can affect its operational efficiency directly. Therefore, how to describe the state of the network structure quantitatively is a key issue to study the macro characteristics and operational law of complex networks. As a description on the state of network structure, network structure entropy provides the measurement to describe the state of the network structure quantitatively.In reality, the majority of the networks are dynamic and in the process of evolution. The existing literature on network structure entropy does not consider the dynamic development of the network. Research on dynamic network structure entropy is still rare relatively. A large number of empirical studies have shown that the majority of the network has scale-free characteristics. BA model as the basic model of scale-free networks, it put forward the growth and preferential attachment mechanism which can depict the way to generate the scale-free networks. Therefore, this paper proposes an issue of the dynamic network structure entropy measurement based on the BA model, classifies the mechanism of growth, and gives the methods of the dynamic network structure entropy measurement based on the different ways of the growth and the preferential attachment. The main work is summarized as follows:(1) Proposed the problem of the dynamic network structure entropy measurement. Considering the characteristics of the networks’dynamic development, the problem of the dynamic network structure entropy measurement is proposed. Based on the previous studies, a general method of dynamic network structure entropy measurement is proposed from the perspectives of the nodes and the relationships among them.(2) Proposed the research framework of measurement of dynamic network structure entropy based on the BA model. The research frameworks of dynamic network structure entropy measurement based on the classification of the growth and preferential attachment mechanism are proposed.(3) Come up with the method of the dynamic network structure entropy measurement based on of the linear growth and the preferential attachment. The variation of the node degree and the shortest path length in the network structure are analyzed under the mechanism of the linear growth and the preferential attachment. Then, come up with the method of the dynamic network structure entropy measurement based on the linear growth and the preferential attachment combining with the general method of the dynamic network structure entropy measurement.(4) Come up with the method of dynamic network structure entropy measurement based on of the nonlinear growth and the preferential attachment. Considering two ways of the nonlinear growth (the power-law growth and the exponential growth), the variation of node degree and the shortest path length in the network structure is analyzed respectively. Then, the calculation methods of the node degree and the length of the shortest path are given. Based on this, the methods of the dynamic network structure entropy measurement based on of these two ways are proposed.This thesis not only provides some reference for the measurement of the dynamic network structure state in the scale-free network, but also enriches the existing entropy measurement methods and the application of entropy theory on the field of complex network. In addition, this thesis can also provide some ideas for related research.