Significance-based community detection in weighted networks

Area of Science:

• Network Science
• Statistical Physics
• Data Mining

Background:

• Community detection in un-weighted networks often relies on null models for statistical significance.
• Weighted networks present unique challenges for community detection due to edge weights.
• Existing methods may struggle with overlapping communities and background noise in weighted networks.

Purpose of the Study:

• Introduce a novel null model for weighted networks: the continuous configuration model.
• Develop a statistically grounded community detection algorithm for weighted networks.
• Benchmark the performance of the new method against existing approaches.

Main Methods:

• Propose a community extraction algorithm using iterative hypothesis testing under the continuous configuration model.
• Prove a central limit theorem for edge-weight sums and asymptotic consistency under a weighted stochastic block model.
• Incorporate the algorithm into the CCME (Community Clustering with a Model-based Expectation) method.

Main Results:

• CCME shows competitive empirical performance in simulations, particularly with overlapping communities and background nodes.
• The continuous configuration model provides a robust null hypothesis for weighted network analysis.
• Analysis of real-world networks reveals macro-features of systems with potential background nodes.

Conclusions:

• The continuous configuration model and CCME offer a statistically sound approach to community detection in weighted networks.
• CCME is effective in identifying communities even in the presence of noise and overlapping structures.
• The method provides valuable insights into the organization of complex systems represented by weighted networks.