Network Stability Study

The stability of networks is studied in this paper. And this paper is divided into three parts. The first part reviews some basic knowledge related networks. The second part researches 2-stable networks. The third part focuses on a model of pairwise stable networks and a model of individually stable networks.Firstly, the knowledge of networks and complex networks is introduced. Social network is studied mainly in this paper. In the process of researching on social networks, the stability of networks is important factor to judge which network is good or not.Secondly, the network model is information sharing model of social network. A k-stable network is constructed by k-defection. On the basis of concepts and properties of the independent set and the clique, the paper researches the properties of a special network and obtains an excellent algorithm, and then constructs a 2-stable network whose price of stability is equal to 1. In addition, the connections of graph coloring and a 2-stable network are found by researching on the properties of the graph coloring. All the results provide an important idea for further research on the stability of networks.Thirdly, the stability of two network models is researched mainly. The first network model is based on Jackson and Wolinsky's JW model. With the change of time and individuals, a dynamic framework for the analysis of network formation is proposed and the stability of a model of dynamic networks is put forward. The second network model is a specific non-cooperative model and individual stability is raised. According to the research of individual stability, the condition of stability about the given star network and complete network is got. And the condition is extended to the general star network and complete network.