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Significance-based community detection in weighted networks.

John Palowitch1, Shankar Bhamidi1, Andrew B Nobel1

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Summary

This study introduces a new null model for weighted networks, enabling statistically significant community detection. The proposed CCME method demonstrates competitive performance, especially with overlapping communities and background nodes.

Keywords:
Community detectionMultiple testingNetwork modelsUnsupervised learningWeighted networks

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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.