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A DC programming approach for finding communities in networks.

Hoai An Le Thi1, Manh Cuong Nguyen, Tao Pham Dinh

  • 1Laboratory of Theoretical and Applied Computer Science, University of Lorraine, Ile du Saulcy, 57045 Metz, France hoai-an.le-thi@univ-lorraine.fr.

Neural Computation
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Summary
This summary is machine-generated.

A new algorithm, DCAM, efficiently discovers community structures in complex networks by maximizing modularity. This method automatically identifies the optimal number of communities, outperforming existing approaches in speed and scalability.

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Area of Science:

  • Network Science
  • Computational Physics
  • Data Mining

Background:

  • Community structure discovery is crucial across various scientific fields.
  • Modularity, proposed by Newman and Girvan (2004), is the standard metric for network community evaluation.
  • The modularity maximization problem seeks the optimal network partition for highest modularity.

Purpose of the Study:

  • To introduce DCAM, a novel algorithm for the modularity maximization problem.
  • To develop a fast, scalable, and accurate method for automatic community discovery in large networks.

Main Methods:

  • DCAM utilizes difference of convex (DC) programming and DC algorithms (DCA) within a nonconvex programming framework.
  • The algorithm is optimized for efficiency, requiring only a matrix-vector product per iteration.
  • DCAM automatically determines the optimal number of communities during its iterative process.

Main Results:

  • DCAM successfully identified optimal partitions and the optimal number of communities in extensive real-world network datasets.
  • Experiments on networks with millions of nodes and edges demonstrated DCAM's superior performance compared to reference algorithms.
  • The algorithm showed significant advantages in solution quality, speed, and scalability.

Conclusions:

  • DCAM offers an effective and efficient solution for the modularity maximization problem.
  • The algorithm provides a strong balance between solution accuracy and computational runtime.
  • DCAM represents a significant advancement in automatic community discovery for complex networks.