  In the study of complex networks almost all theoretical models have the
property of infinite growth, but the size of actual networks is finite.
According to statistics from the China Internet IPv4 (Internet Protocol version
4) addresses, this paper proposes a forecasting model by using S curve
(Logistic curve). The growing trend of IPv4 addresses in China is forecasted.
There are some reference value for optimizing the distribution of IPv4 address
resource and the development of IPv6. Based on the laws of IPv4 growth, that
is, the bulk growth and the finitely growing limit, it proposes a finite
network model with a bulk growth. The model is said to be an S-curve network.
Analysis demonstrates that the analytic method based on uniform distributions
(i.e., Barab\'asi-Albert method) is not suitable for the network. It develops
an approximate method to predict the growth dynamics of the individual nodes,
and use this to calculate analytically the degree distribution and the scaling
exponents. The analytical result agrees with the simulation well, obeying an
approximately power-law form. This method can overcome a shortcoming of
Barab\'asi-Albert method commonly used in current network research.
