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Clustering in complex directed networks.

Giorgio Fagiolo1

  • 1Sant'Anna School of Advanced Studies, Laboratory of Economics and Management, Piazza Martiri della Libertà 33, I-56127 Pisa, Italy. giorgio.fagiolo@sssup.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
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This study generalizes the clustering coefficient (CC) for directed networks, offering new ways to measure network clustering. The findings are illustrated using world-trade flow data.

Area of Science:

  • Network Science
  • Graph Theory
  • Data Analysis

Background:

  • Empirical networks often exhibit clustering, forming interconnected groups of nodes.
  • The clustering coefficient (CC) quantifies this tendency in undirected graphs.
  • Previous generalizations extended CC to weighted, undirected networks.

Purpose of the Study:

  • To extend the clustering coefficient (CC) to directed networks, both binary and weighted.
  • To compute the expected CC for random directed graphs.
  • To differentiate CC measures based on triangle orientation (all triangles vs. cycles).

Main Methods:

  • Generalization of the clustering coefficient (CC) for directed graphs.
  • Calculation of expected CC values for random directed graph models.

Related Experiment Videos

  • Application of the extended CC to empirical world-trade flow data.

    • Main Results:

    • Developed novel clustering coefficient (CC) metrics for directed networks.
    • Distinguished between CC measures that consider all directed triangles and those focusing on cycles.
    • Demonstrated the utility of the extended CC using real-world trade flow data.

    Conclusions:

    • The generalized clustering coefficient (CC) provides a robust measure for directed networks.
    • The new metrics offer deeper insights into network structure and clustering patterns.
    • This work advances the analysis of complex systems, including economic networks.