Study Of The Degree Distribution Of Accelerated Growing Model About Complex Networks

Complex network is the powerful tool in the investigating to complex systems. Recently, the investigating to complex networks attracts more and more attention. Based on the fact that the degree distribution of many real complex networks displays power law format, Barabás and Albert proposed the revolutionary BA model of scale-free networks in 1999. As growing and preferential attachment mechanisms are incorporated in the evolution of BA network model, so the degree distribution of this model follows the power law format. The degree distribution of network reflects the hints of topology of the whole networks, the accelerated growing way of networks is one of the very important growing ways, so the investigation to accelerated growing networks is very important. In this paper, according to the real networks'characteristic, we propose a accelerated growing model, which not only contains the exterior growth, but also includes the interior growth, using mean-field theory calculate the degree distribution of the accelerated growing networks, achieve that it is a scale-free networks. using nonequilibrium statistic method, we give the master equation satisfied by degree distribution of the model in differential format, and obtain its rigorous analytical solution. The obtained solution is composed of two terms. At given finite time, one term decays as power law way, well the other reflects the size effect. At infinite time of the evolution of this model, the normalized degree distribution is well accord with using mean-field theory.