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Quantitative function for community detection.

Zhenping Li1, Shihua Zhang, Rui-Sheng Wang

  • 1Beijing Wuzi University, Beijing, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
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We introduce modularity density (D value), a new quantitative function for community detection. This method outperforms existing approaches, accurately identifying detailed modules and the correct number of communities.

Area of Science:

  • Network science
  • Data mining
  • Computational social science

Background:

  • Community detection is crucial for understanding complex systems.
  • Existing methods like modularity (Q) have limitations in resolving fine-grained structures and determining community count.
  • There is a need for improved quantitative functions for robust community partitioning.

Purpose of the Study:

  • To propose a novel quantitative function for community partition, termed modularity density (D value).
  • To demonstrate the superiority of modularity density over the widely used modularity Q.
  • To establish the equivalence of modularity density with the objective function of kernel k-means.

Main Methods:

  • Development of the modularity density (D value) as a quantitative measure for community partition.

Related Experiment Videos

  • Theoretical analysis to prove the equivalence with kernel k-means objective function.
  • Numerical simulations and comparative analysis against existing community detection methods.

    • Main Results:

    • Modularity density (D value) is shown to be a superior quantitative function for community partition compared to modularity Q.
    • Optimizing modularity density allows for the resolution of detailed community modules missed by existing approaches.
    • The new criterion effectively and correctly identifies the number of communities within a network.

    Conclusions:

    • Modularity density (D value) offers a more effective and accurate approach to community detection in complex networks.
    • This novel function overcomes limitations of previous methods, enabling finer resolution and accurate community number identification.
    • The equivalence with kernel k-means suggests broader applicability in machine learning and data analysis.