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Recursive graphs with small-world scale-free properties.

Francesc Comellas1, Guillaume Fertin, André Raspaud

  • 1Department de Matemàtica Aplicada IV, EPSC, Universitat Politècnica de Catalunya, Avinguda Canal Olímpic s/n, 08860 Castelldefels, Barcelona, Catalonia, Spain. comellas@mat.upc.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2004
PubMed
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Recursive clique trees exhibit small-world and scale-free properties, allowing tunable clustering and power-law exponents. These graphs offer a generalized construction for network analysis with controllable characteristics.

Area of Science:

  • Graph theory
  • Network science
  • Complex systems

Background:

  • Small-world networks exhibit high clustering and short path lengths.
  • Scale-free networks possess a power-law degree distribution, common in real-world systems.
  • Recursive constructions offer novel ways to generate complex graph structures.

Purpose of the Study:

  • Introduce and analyze recursive clique trees.
  • Investigate their small-world and scale-free properties.
  • Explore the tunability of their clustering and degree distribution.

Main Methods:

  • Characterization of graph properties including diameter, degree distribution, and clustering parameter.
  • Analysis of the recursive structure of the proposed graphs.
  • Comparison with existing graph construction methods.

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Main Results:

  • Recursive clique trees demonstrate both small-world and scale-free characteristics.
  • The clustering parameter and power-law exponent are finely tunable.
  • These graphs generalize previous constructions with fixed degree distributions.

Conclusions:

  • Recursive clique trees provide a versatile model for complex networks.
  • Their tunable properties allow for fine-grained control in network design.
  • This framework offers a generalized approach to constructing networks with desired attributes.