Empirical Reference Distributions for Networks of Different Size

Area of Science:

• Network analysis
• Ecological networks
• Graph theory

Background:

• Network analysis is widely used across scientific fields.
• Comparing network statistics across networks of varying sizes presents significant challenges.
• Existing normalization methods for network statistics are often insufficient.

Purpose of the Study:

• To address the limitations of direct comparison and existing normalization methods for network statistics.
• To propose and validate a novel adjustment method for comparing network statistics across different network sizes.
• To apply the new methodology to real-world ecological network data.

Main Methods:

• Simulations were used to demonstrate the inappropriateness of direct comparison of network statistics.
• A reference distribution based on a mixture model of random graphs was developed.
• Bernoulli models were employed as mixture components for constructing the reference distribution.
• The proposed adjustment method was applied to ecological networks from the Los Angeles Family and Neighborhood Survey.

Main Results:

• Direct comparison of network statistics across different network sizes is often inappropriate.
• Normalization relative to a simple reference distribution offers improvement but remains problematic.
• The proposed mixture model-based adjustment method provides comparable network statistics across varying sizes.
• The method is computationally efficient and captures relevant network features.

Conclusions:

• A novel and computationally efficient method for adjusting network statistics enables reliable cross-network comparisons.
• The methodology is effective for analyzing structural features in ecological networks of different sizes.
• This approach enhances the validity of network analysis findings across diverse network structures.