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Finding community structure using the ordered random graph model.

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This study introduces a new algorithm for ordering network matrices. The method improves the visualization of community structures, revealing network components more clearly than existing techniques.

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Area of Science:

  • Network science
  • Graph theory
  • Data visualization

Background:

  • Adjacency matrix visualization reveals network macroscopic features.
  • Community structure, characterized by dense components, appears as a block-diagonal form.
  • Classical ordering algorithms struggle to align matrices for visible community structure.

Purpose of the Study:

  • To develop a novel ordering algorithm for adjacency matrices.
  • To enhance the visibility of community structures in networks.
  • To outperform existing ordering algorithms in identifying network communities.

Main Methods:

  • Proposed an ordering algorithm based on maximum-likelihood estimation.
  • Utilized an ordered random graph model for matrix element alignment.
  • Compared the proposed method against classical ordering algorithms.

Main Results:

  • The proposed algorithm effectively aligns matrix elements.
  • Community structures become more clearly identifiable.
  • Demonstrated superior performance in community structure detection compared to existing methods.

Conclusions:

  • The novel ordering algorithm enhances network visualization.
  • Maximum-likelihood estimation provides an effective approach for matrix ordering.
  • This method offers improved identification of community structures in complex networks.