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A stochastic model for detecting overlapping and hierarchical community structure.

Xiaochun Cao1, Xiao Wang2, Di Jin2

  • 1School of Computer Science and Technology, Tianjin University, Tianjin 300072, China; State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China.

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This study introduces a new method for detecting overlapping communities in complex networks. The approach automatically determines the number of communities and reveals hierarchical structures without prior information.

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Area of Science:

  • Network science
  • Data mining
  • Computational social science

Background:

  • Community detection is crucial for understanding complex networks.
  • Existing methods often require predefined community numbers or sizes, limiting real-world applicability.
  • Overlapping community detection is essential as network nodes can belong to multiple groups.

Purpose of the Study:

  • To develop a practical algorithm for overlapping community detection.
  • To enable automatic determination of the number of communities.
  • To reveal the hierarchical structure of complex networks.

Main Methods:

  • A generative model using Nonnegative Matrix Factorization (NMF) with l(2,1) norm regularization.
  • The NMF provides soft membership for overlapping communities.
  • l(2,1) regularization automatically determines community count, and a resolution parameter explores hierarchy.

Main Results:

  • The proposed method successfully identifies overlapping community structures.
  • It automatically determines the number of communities without prior input.
  • The algorithm effectively reveals hierarchical network structures.
  • Empirical validation on synthetic and real-world networks demonstrates superior performance compared to state-of-the-art methods.

Conclusions:

  • The developed generative model offers a robust solution for overlapping community detection.
  • The method's ability to automatically determine community numbers and reveal hierarchy enhances its practical utility.
  • This approach advances the analysis of complex network structures.