Topological Analysis Of Acceleratingly Growing Weighted Complex Network Models With Local Information

Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, three weighted network models with local information and accelerating growth are proposed. They are the acceleratingly growing weighted network model with local information and the same types of nodes, the acceleratingly growing weighted network model with local information and different types of nodes, the acceleratingly growing weighted network model with local information which can describe the stock markets approximatively. In the first model, analytical expressions are derived for the evolutions and distributions of strength and weight, which are relevant to accelerating growth. The distribution of strength displays scale-free form. When the size of the acceleration parameterθis regulated, the distribution of weight also displays scale-free form. In the second model, we derive analytical expressions for the evolutions and distributions for strength and weight, which are relevant to accelerating growth. We study the distributions of the strength and edge weight. Interestingly, the distributions for strength and weight display scale-free form. In the third model, because there are many stockholders in the stock markets, and they holds the same or different kinds of stocks. So some stockholders have relation to each other when they holds the same kinds of stocks. And when the same kinds of stocks they hold become more, the relation among them become closer. And vice versa. To study the stock markets, we derive analytical expressions for the evolutions and distributions for strength and edge weight, which are relevant to accelerating growth. Westudy the distributions of the strength and edge weight. Interestingly, when p₃ = p₅ = 0, the distribution for strength displays scale-free form. When p₂= p₃= p₅=0 ,the distribution foredge weight displays scale-free form. Or when p₃ = p₅ = 0, the size of the acceleration parameter 6 is regulated, the distribution for edge weight also displays scale-free form.