Time evolution of the degree distribution of model A of random attachment growing networks

For random growing networks, Barabás and Albert proposed a kind of model in Barabás et al. [Physica A 272 (1999) 173], i.e. model A. In this paper, for model A, we give the differential format of master equation of degree distribution and obtain its analytical solution. The obtained result P(k, t) is the time evolution of degree distribution. P(k, t) is composed of two terms. At given finite time, one term decays exponentially, the other reflects size effect. At infinite time, the degree distribution is the same as that of Barabás and Albert. In this paper, we also discuss the normalization of degree distribution P(k, t) in detail.