Abstract: Vertex degree distribution is an important parameter to evaluate the local property of vertices and connectivity between the vertex and other vertices in the network. An extended growth evolving model was proposed by adding new vertices or new edges using nonlinear preferential attachment rule at each time step. Moreover, the vertex degree distribution expression via the probability methods was calculated, and it was found that some existing network model is one of special cases of the model, the corresponding vertex degree distribution can also be obtained by the vertex degree distribution expression of the model. The expression to obtain the corresponding vertex degree distribution was also used and the numerical simulations for network models of two different vertex weighted functions was designed. Experiments indicate that the numerical simulations are coincide with our theoretical results well.

Key words: vertex degree distribution, nonlinear preferential attachment, vertex weighted function