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Detecting communities using asymptotical surprise.

V A Traag1,2, R Aldecoa3, J-C Delvenne4,5

  • 1Royal Netherlands Institute of Southeast Asian and Caribbean Studies, Leiden, The Netherlands.

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Summary
This summary is machine-generated.

We developed an approximation for the surprise metric to detect network communities. This method is more discriminative than modularity, especially for many small communities, and works for weighted graphs.

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Area of Science:

  • Network science
  • Graph theory
  • Data analysis

Background:

  • Real-world networks often exhibit community structures.
  • Existing methods for community detection rely on objective functions, which define communities implicitly.
  • The 'surprise' metric is a recently proposed measure for assessing network partition quality.

Purpose of the Study:

  • To analyze and approximate the 'surprise' metric for community detection.
  • To develop an efficient algorithm for optimizing surprise.
  • To compare surprise with other methods, particularly modularity.

Main Methods:

  • Developed an accurate asymptotic approximation for the surprise metric.
  • Created an efficient algorithm for optimizing surprise based on the approximation.
  • Extended the surprise metric to weighted graphs.
  • Compared surprise to modularity, analyzing their performance in different network scenarios.

Main Results:

  • The approximation allows for efficient surprise optimization and extension to weighted graphs.
  • Surprise is largely unaffected by the resolution limit, a known issue with modularity.
  • Surprise may overestimate communities, while modularity may underestimate them.
  • Surprise excels in detecting many small communities, whereas modularity performs better with few large communities.

Conclusions:

  • The approximated surprise metric offers a more discriminative approach to community detection compared to modularity.
  • Surprise can identify community structures that modularity might miss, particularly in networks with numerous small clusters.
  • The developed methods provide a robust and efficient tool for analyzing network community structures.