The Research For Weighted Network Modeling

Complex network is a new subject to study the complex system. Domestic and foreign scholars have been playing much attention to it recently. As each complex system can be abstracted to a network consisting of the interactional individuals, network exist every where in our life. The research of complex network, especially the function and topology of it, has great influence to our life. In this paper, combining the character and research status of the complex network, we give several weighted network model and make some analysis about it. The main work is as follow:Firstly, considering the influence of new joined arrow to the topology and weight evolution mechanism comparing with BA model, we construct a weighted network model. It shows that the distribution of degree and weight follows power law, having the big tail, and the distribution index can be adjusted with parameter w. Comparing with BA model that the distribution index is three, it has a universal application and can meet most of the real network.Secondly, considering the distance to the preference in space and the mechanism of weight evolution, we expand the preference mechanism to the two-dimensional space and construct a special weighted network. Adjusting the parameter r, we found an interesting phenomenon. When r is small, the network mainly acts as scale-free property, while r is big enough, it mainly acts as small-world property.Thirdly, applying evolutionary game to complex network modeling, we construct a scale-free weighted network with high cooperation level. In our model, it has a learning mechanism based on preference and historical information of its own. Then, we expanded the avail matrix to three-dimension, and ussed the existence and stability of species. Finally, it comes to be a conclusion that it has Nash Equilibrium among the species.