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Network clustering coefficient without degree-correlation biases.

Sara Nadiv Soffer1, Alexei Vázquez

  • 1Department of Mathematics, Rutgers University Piscataway, New Jersey 08854, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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The clustering coefficient, a measure of network connectivity, does not inherently indicate hierarchy. Our findings reveal that degree-correlation biases in its definition create this illusion, suggesting a constant or logarithmic decay in real networks.

Area of Science:

  • Network Science
  • Graph Theory
  • Complex Systems Analysis

Background:

  • The clustering coefficient measures the interconnectedness of a vertex's neighbors in a graph.
  • A decreasing clustering coefficient with vertex degree is often interpreted as evidence of hierarchical network structures.
  • This interpretation has been a long-standing assumption in network analysis.

Purpose of the Study:

  • To investigate the influence of degree-correlation biases on the clustering coefficient definition.
  • To introduce a revised clustering coefficient definition that filters out these biases.
  • To re-evaluate the relationship between clustering coefficient and vertex degree in real-world networks.

Main Methods:

  • Analysis of existing clustering coefficient definitions.

Related Experiment Videos

  • Development of a new clustering coefficient metric accounting for degree correlations.
  • Empirical testing of the new metric on various real-world network datasets.

    • Main Results:

    • The observed decrease in clustering coefficient with vertex degree is an artifact of the standard definition's inherent degree-correlation biases.
    • The newly introduced, bias-filtered clustering coefficient shows different behavior in real networks.
    • In real networks, the bias-filtered clustering coefficient remains constant or exhibits logarithmic decay with vertex degree.

    Conclusions:

    • The signature of hierarchical structure in real networks is not an intrinsic property but a consequence of the clustering coefficient's definition.
    • A revised clustering coefficient definition provides a more accurate representation of network topology.
    • Network analysis should account for degree-correlation biases when interpreting clustering coefficients.