How rare are power-law networks really?
I Artico1, I Smolyarenko2, V Vinciotti2
1Università della Svizzera italiana, Lugano, Switzerland.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 19, 2020
Summary
Real-world networks often follow a power-law structure. A new statistical method confirms that nearly 65% of networks exhibit this power-law degree distribution, suggesting a common network law.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Real-world networks exhibit scale-free properties, suggesting underlying universal network laws.
- Testing for power-law degree distributions has been contentious due to statistical challenges.
Purpose of the Study:
- To develop a robust statistical testing procedure for network degree distributions.
- To specifically test for power-law tails consistent with the de Solla Price model.
Main Methods:
- Modified the Kolmogorov-Smirnov test for enhanced tail sensitivity.
- Accounted for dependent degree sequences and insufficient statistical power in finite networks.
- Applied the novel test to numerous empirical network degree distributions.
Main Results:
- The proposed method effectively tests for power-law tails in network degree distributions.
- Power-law degree distributions were found to be common, not rare.
- Approximately 65% of tested networks were classified as having a power-law tail with high statistical power (≥80%).
Conclusions:
- The prevalence of power-law degree distributions supports the existence of fundamental network laws.
- The developed statistical test provides a reliable tool for analyzing network structures.
- Findings challenge previous skepticism regarding the widespread occurrence of power-law networks.
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