Carrying Capacity in Barabási-Albert Network

The effect of finiteness in degree number is analyzed on a growing network. The dynamics is governed by a rule where the degree number increases under a scheme similar to the Malthus-Verhulst model in the context of population growth. One notices that the second moment of degree is closely related to the linking probability of this growing network. The degree distribution is analyzed in both stationary and time-dependent regimes through some exact results and simulations, and a scaling behaviour is found in asymptotically large time.