Finite-size effects in Barabasi-Albert growing networks

We investigate the influence of the network's size on the degree distribution pi(k) in Barabasi-Albert model of growing network with initial attractiveness. Our approach based on moments of pi(k) allows us to treat analytically several variants of the model and to calculate the cutoff function, giving finite-size corrections to pi(k). We study the effect of initial configuration as well as of addition of more than one link per time step. The results indicate that asymptotic properties of the cutoff depend only on the exponent gamma in the power-law describing the tail of the degree distribution. The method presented in this paper is very general and can be applied to other growing networks.