Graphlet correlation distance to compare small graphs.

Area of Science:

• Graph theory
• Network analysis
• Statistical modeling

Background:

• Graph models are standard for representing relationships between entities.
• Existing methods like Graphlet Correlation Distance (GCD) are well-established for large graphs.
• Small graphs with high connection densities are less explored but relevant in sociology, ecology, and fisheries.

Purpose of the Study:

• To investigate the distinguishability of common graph models (Erdős-Rényi, Scale-Free, Small-World, Geometric) using a specific GCD measure (GCD11).
• To develop and apply a randomization statistical test based on GCD11 for comparing empirical graphs against null models.
• To analyze pairwise proximity in a fishing vessel case study.

Main Methods:

• Numerical experiments to evaluate GCD11's ability to distinguish graph models based on density and order.
• Development of a randomization statistical test utilizing GCD11.
• Application of the statistical test to empirical data from a fishing fleet.

Main Results:

• Identified conditions under which different graph models can be distinguished by GCD11.
• The statistical test ruled out the assumption of independent pairing within the studied fishing fleet.
• Demonstrated the challenges in identifying similarities between real-world small graphs and theoretical graph models.

Conclusions:

• GCD11 provides a method for distinguishing between various small graph models.
• The developed statistical test offers a novel approach for analyzing empirical network data.
• Findings from the fishing case study have implications for understanding vessel interactions and challenging existing assumptions in fisheries science.