Estimating the Number of Communities in Weighted Networks

Area of Science:

• Network Science
• Data Mining
• Statistical Physics

Background:

• Community detection is crucial for understanding network structure.
• Existing methods often require the number of communities to be predefined.
• Accurately determining community numbers in weighted networks remains an open problem.

Purpose of the Study:

• To propose a novel method for estimating the number of communities in weighted networks.
• To address limitations of existing methods that assume a known number of communities.
• To provide a robust approach for networks with arbitrary distributions and negative edge weights.

Main Methods:

• Combining weighted modularity with spectral clustering.
• Applying the method to weighted networks under a degree-corrected distribution-free model.
• Handling networks with negative and signed edge weights.

Main Results:

• The proposed method accurately estimates the number of communities.
• Demonstrated superior performance compared to existing methods numerically and empirically.
• Successfully applied to networks with negative and signed edge weights.

Conclusions:

• The developed approach effectively determines the number of communities in weighted networks.
• Offers a flexible and accurate solution for complex network analysis.
• Advances the field of community detection in weighted and signed networks.