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

TL;DR

This paper models the growth of real-world finite networks like IPv4 addresses using an S-curve, proposing an approximate analytical method to predict degree distributions that improves upon existing models.

Contribution

It introduces an S-curve network model for finite growth and develops an approximate analytical method to predict degree distributions, surpassing the Barabási-Albert approach.

Findings

The model accurately predicts IPv4 address growth trends.

The analytical degree distribution follows an approximate power-law.

The method aligns well with simulation results.

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 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.