A nature inspired modularity function for unsupervised learning involving spatially embedded networks.

Area of Science:

• Network Science
• Statistical Physics
• Data Analysis

Background:

• Network clustering quality is typically assessed using modularity.
• Modularity compares network clusters to a random graph null model.
• Standard modularity is ill-suited for spatially embedded networks due to its lack of geometrical considerations.

Purpose of the Study:

• To propose a novel variant of modularity for analyzing spatially embedded networks.
• To develop a method that does not rely on a null model for network clustering.
• To improve the detection of physically meaningful partitions and hierarchical structures in networks.

Main Methods:

• Developed a null-model-free variant of the modularity metric.
• Analyzed networks generated from granular ensembles to test the new method.
• Compared the performance of the proposed method against the Newman-Girvan (NG) modularity.

Main Results:

• The proposed modularity variant demonstrated superior performance in detecting optimal partitions in granular ensemble networks.
• The new method effectively identified physically transparent partitions, unlike standard modularity.
• The approach successfully detected hierarchical structures within the analyzed networks.

Conclusions:

• The developed null-model-free modularity measure is a more suitable metric for spatially embedded networks.
• This method enhances the identification of meaningful community structures and hierarchies in complex systems.
• The findings suggest a significant improvement over existing modularity-based network analysis techniques.