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Filipi N Silva1, Aiiad Albeshri2, Vijey Thayananthan2

  • 1Indiana University Network Science Institute (IUNI), Bloomington, Indiana, 47408, USA.

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Summary
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We introduce robustness modularity, a new metric for network community detection. This measure assesses network modularity by evaluating the probability of finding trivial partitions under random network perturbations, offering improved interpretability over the Girvan-Newman function.

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Area of Science:

  • Network Science
  • Data Mining
  • Graph Theory

Background:

  • Assessing network modularity is crucial for community detection.
  • The Girvan-Newman (GN) modularity function is standard but has interpretability issues.
  • GN modularity can yield high values for random networks lacking community structure.

Purpose of the Study:

  • To propose a new, interpretable modularity measure based on robustness.
  • To introduce alternative quality functions with lower time complexity.
  • To enable robust assessment and comparison of community structure strength in networks.

Main Methods:

  • Developed a robustness modularity measure based on the probability of trivial partitions under random network perturbation.
  • Implemented the measure for clustering algorithms detecting absence of group structure.
  • Introduced modularity difference and information modularity as alternative quality functions.

Main Results:

  • Robustness modularity effectively assesses and compares community structure strength in artificial and real networks.
  • Modularity difference and information modularity correlate strongly with robustness modularity.
  • The alternative measures offer lower time complexity for large-scale network analysis.

Conclusions:

  • Robustness modularity provides a more interpretable assessment of network modularity.
  • Alternative modularity measures offer computational advantages for large networks.
  • The proposed methods enhance the evaluation of community detection algorithms.