Universality of competitive networks for weighted networks

Abstract: In this paper, we propose a new model that allows us to investigate this competitive aspect of real networks in quantitative terms. Through theoretical analysis and numerical simulations, we find that the competitive network have the universality for a weighted network. The relation between parameters in the weighted network and the competitiveness in the competitive network is obtained. So we can use the expression of the degree distribution of the competitive model to calculate that and the strength of the weighted network directly. The analytical solution reveals that the degree distribution of the weighted network is correlated with the increment and initial value of edge weights, which is verified by numerical simulations. Moreover, the evolving pattern of a clustering coefficient along with network parameters such as the size of a network, an updating coefficient, an initial weight and the competitiveness are obtained by further simulations. Specially, it is necessary to point out that the initial weight plays equally significant role as updating coefficient in influencing the topological characteristics of the network.