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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.