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Scale invariance and statistical significance in complex weighted networks.

Filipi N Silva1,2, Sadamori Kojaku3, Alessandro Flammini2

  • 1Northwestern University, Center for Science of Science and Innovation, Evanston, Illinois 60208, USA.

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Summary

The weighted configuration model (WCM) for randomizing networks shows scale-dependent results. A new two-step method ensures scale-invariant and unbiased significance assessments for weighted network analysis.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Real-world networks often feature weighted edges representing interaction strength.
  • Network randomization is crucial for assessing statistical significance of network properties.
  • The weighted configuration model (WCM) is a common method for weighted network randomization.

Purpose of the Study:

  • To investigate the scale dependency of the weighted configuration model (WCM).
  • To develop a method for unbiased statistical significance assessment in weighted networks.
  • To ensure results are independent of the chosen weight scale.

Main Methods:

  • Analysis of the scale dependency of the weighted configuration model (WCM).
  • Implementation of a two-step approach: structure randomization followed by weight randomization.
  • Utilizing a suitable distribution for weight randomization to achieve scale invariance.

Main Results:

  • The weighted configuration model (WCM) produces scale-dependent statistical significance.
  • The proposed two-step approach restores scale invariance to weighted network randomization.
  • This method enables unbiased significance assessments for weighted network properties.

Conclusions:

  • The traditional weighted configuration model (WCM) can lead to biased significance assessments due to scale dependency.
  • A novel two-step randomization approach ensures scale invariance and reliable statistical significance evaluation for weighted networks.
  • This work provides a robust framework for analyzing complex weighted networks across various scientific domains.