Scale invariance and statistical significance in complex weighted networks.

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.