Inferring meaningful communities from topology-constrained correlation networks

Area of Science:

• Graph theory
• Network analysis
• Data science

Background:

• Community structure detection is crucial for understanding complex networks.
• Optimizing modularity scores is a common method for community detection.
• Topological constraints in correlation graphs can lead to over-fragmentation of communities.

Purpose of the Study:

• To address the over-fragmentation issue in community detection caused by topological constraints.
• To propose and validate a novel refinement method combining modularity optimization with Linear Discriminant Analysis (LDA) and statistical significance testing.
• To evaluate the performance of the proposed method on both simulated and empirical datasets.

Main Methods:

• Community detection via modularity optimization.
• Refinement of community structures using Linear Discriminant Analysis (LDA).
• Application of a statistical test for significance.
• Validation on simulated data with topological constraints and empirical datasets (US Senate voting, protein structures).

Main Results:

• The proposed LDA-based refinement method outperforms modularity optimization alone in topology-constrained simulations.
• Analysis of US Senate voting data revealed regional biases transcending party affiliations, indicating sub-structures within communities.
• For the biological dataset, LDA filtering did not alter results when topological constraints were present, suggesting robustness.

Conclusions:

• The LDA-based refinement effectively mitigates over-fragmentation in community detection caused by topological constraints.
• The method demonstrates robustness, not negatively impacting results when over-fragmentation is not an issue.
• The approach offers a valuable tool for analyzing complex networks, uncovering nuanced patterns in diverse datasets.