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Related Experiment Videos

Clustering in complex networks. I. General formalism.

M Angeles Serrano1, Marián Boguñá

  • 1School of Informatics, Indiana University, Eigenmann Hall, 1900 East Tenth Street, Bloomington, IN 47406, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
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We introduce edge multiplicity to quantify clustering in complex networks, extending the clustering coefficient. This reveals two distinct network transitivity classes: weak and strong, impacting network properties.

Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • Complex networks exhibit intricate structures beyond simple connections.
  • Understanding network clustering is crucial for analyzing their behavior and properties.

Purpose of the Study:

  • To develop a comprehensive theoretical framework for analyzing clustering in complex networks.
  • To introduce novel metrics for characterizing transitive relations within networks.

Main Methods:

  • Development of the 'edge multiplicity' concept to measure triangle participation in edges.
  • Definition of a three-vertex correlation function as a fundamental network property.
  • Application of the developed formalism and metrics to analyze real-world networks.

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Main Results:

  • Introduction of edge multiplicity, a measure extending the clustering coefficient by considering two vertices.
  • Definition of a three-vertex correlation function for describing clustered network properties.
  • Identification of two main classes of clustered networks: weak transitivity (low edge multiplicity, disjoint triangles) and strong transitivity (high edge multiplicity, shared edges).

Conclusions:

  • The new theoretical approach and metrics provide a thorough characterization of transitive relations in networks.
  • The classification into weak and strong transitivity classes offers new insights into network organization.
  • Network transitivity class has significant implications for network percolation properties, a topic for future research.