Finite size effects in Barabasi-Albert growing networks
  We investigate the influence of the network's size on the degree distribution in Barabasi-Albert model of growing network with initial attractiveness. Our approach based on spectral moments allows to treat analytically several variants of the model and to calculate the cut-off function giving finite size corrections to the degree distribution. We study the effect of initial configuration as well as of addition more than one link per time step. The results indicate that asymptotic properties of the cut-off depend only on the exponent in the power law describing the tail of the degree distribution. 
B. Waclaw and I. M. Sokolov