Crossover transition in the Fluctuation of Internet

TL;DR

This study empirically investigates the fluctuation of Internet degree growth across different time scales, revealing a crossover from preferential attachment to Gibrat's law, highlighting the need for more comprehensive modeling.

Contribution

It uncovers a previously unreported crossover transition in Internet degree fluctuations from PA to Gibrat's law across multiple time intervals.

Findings

Gibrat's law applies at larger degrees and longer periods.

A crossover from PA to Gibrat's law is observed.

Internal link correlation influences the emergence of Gibrat's law.

Abstract

Gibrat's law predicts that the standard deviation of the growth rate of a node's degree is constant. On the other hand, the preferential attachment(PA) indicates that such standard deviation decreases with initial degree as a power law of exponent $-0.5$. While both models have been applied to Internet modeling, this inconsistency requires the verification of their validation. Therefore we empirically study the fluctuation of Internet of three different time intervals(daily, monthly and yearly). We find a crossover transition from PA model to Gibrat's law, which has never been reported. Specifically Gibrat-law starts from small degree region and extends gradually with the increase of the observed period. We determine the validated periods for both models and find that the correlation between internal links has large contribution to the emergence of Gibrat law. These findings indicate neither PA nor Gibrat law is applicable to the actual Internet, which requires a more complete model theory.