A note on mean-field theory for scale-free random networks

Usually, the BA model describes the growth and preferential attachment of scale-free networks. In this paper we present the G growth model and the Poisson model in order to describe real networks more precisely than the BA model. We recognize that the vertices arrival process is a renewal process. By using the renewal process theory and continuum theory, we calculate the degree distribution and stationary average degree distribution of the models. The consequences are that the stationary average degree distributions of these models are independent of the arrival process of vertices of the networks and the degree distributions are dependent on the arrival process. The advantage of our results is more accurate than that reported in [1, 2, 3]. Furthermore, the flaw of analysis in [1, 2, 3] is modified in this paper.