S-curve networks and an approximate method for estimating degree distributions of complex networks

doi:10.1088/1674-1056/19/12/120503

Abstract 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 values 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., Barabási–Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses 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 Barabási–Albert method commonly used in current network research.

Keywords: complex network scale-free network power-law distribution IPv4 standard logistic curve

Received: 18 March 2009
Revised: 15 July 2010
Accepted manuscript online:

PACS:	02.50.-r	(Probability theory, stochastic processes, and statistics)
	89.75.Hc	(Networks and genealogical trees)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 70871082), and the Shanghai Leading Academic Discipline Project (Grant No. S30504).

Cite this article:

Guo Jin-Li(郭进利) S-curve networks and an approximate method for estimating degree distributions of complex networks 2010 Chin. Phys. B 19 120503

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S-curve networks and an approximate method for estimating degree distributions of complex networks

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