Algorithms Design On Balance Structure In Signed Nerworks

In recent years, with the rapid development of Internet technology, the information communication between people has become more and more convenient, and the exchanges of information in social network are increasingly apparent. For example, when someone check his friend's dynamic content on Weixin, the relationship between A, A's friend and his friend's friend is needed if he want to read other's comment. So this permission function established under full complex network. Nowadays the study about unsigned complex networks has been more in-depth, but the rise of signed network theory in recent years still has further studies space. The signed network is composed with nodes and edges, and each edge has positive or negative side. The positive edge means "friendship, love" and other negative side connecting means "disgust, hostility" and so on. The recent research about this has focus on how to efficiently carry out community detection, and other research is still relatively weak. With the equilibrium theory, this article mainly studies the basic structural properties and balance evolution on completed signed networks.In this paper, the main work includes the following aspects:(1) Randomly generated completed signed networks with different generate value of positive edge. Search the unit triangle structure and get the rule that the generation probability with the unbalance type of triangle obey the power law.(2) From different angles to analyze the weak balance structure on complete signed network. Via the algorithm based on isolated nodes, we found the basic structure on balanced network. Through combinatorial analysis theory, we get the completely solution set about balanced structure, and explore its structural properties. Last, deduced the number of solution set.(3) Explore the completed signed networks' balance structure property, and put forward an algorithm called the dynamic evolution method of matrix in signed network to realize the structure evolution. The method based on matrix-vector, and transforms the problem into single-objective optimization area. Experimental part, we take evolution on randomly generated singed networks, and the results show that the evolution of the method is effective, and displayed that with the different generate value of positive edge, the final equilibrium state has a big difference.(4) Analyze constrained evolution on unbalanced signed network, and obtain the relationship between the initial positive probability on random network and the selection evolution probability. This could help us to optimize the network dynamic evolution of behavior.These studies focus on balance structure in signed nerworks models, especially, complete decomposition model and the network dynamic evolution. Some key issues have been explored, such as network modeling, inference and applications, especially come up with combinatorial analysis theory to decomposition the network. So it is a new attempt for the combination theory to application on the complex network, and so as the matrix on the evolution of the unbalance network.