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Higher-order clustering in networks.

Hao Yin1, Austin R Benson2, Jure Leskovec3

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Summary
This summary is machine-generated.

This study introduces higher-order clustering coefficients to better understand complex network structures beyond simple triangles. These new metrics offer a more comprehensive view of how network edges cluster, revealing deeper insights into real-world networks.

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Area of Science:

  • Network Science
  • Graph Theory
  • Data Analysis

Background:

  • Complex networks exhibit edge clustering, traditionally measured by the clustering coefficient (triangle closure probability).
  • Understanding higher-order structures (beyond triangles) is crucial for a complete network analysis.
  • Existing metrics do not fully capture clustering behavior in higher-order network cliques.

Purpose of the Study:

  • Introduce novel higher-order clustering coefficients to quantify clique closure probabilities.
  • Generalize the traditional clustering coefficient to higher-order network structures.
  • Provide a more comprehensive measure of edge clustering in complex networks.

Main Methods:

  • Definition and derivation of higher-order clustering coefficients.
  • Analysis of coefficient properties under random graph models.
  • Application of coefficients to real-world network datasets.

Main Results:

  • Higher-order clustering coefficients naturally extend the traditional coefficient.
  • Analysis reveals properties and behaviors of these coefficients in random graph models.
  • New insights into the structure of real-world networks were obtained using these coefficients.

Conclusions:

  • Higher-order clustering coefficients offer a more detailed understanding of network topology.
  • These coefficients are valuable tools for analyzing complex systems across various domains.
  • The study advances the quantification of network clustering beyond pairwise relationships.