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Scale-free networks with exponent one.

G Timár1, S N Dorogovtsev1,2, J F F Mendes1

  • 1Departamento de Física da Universidade de Aveiro and I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.

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Summary
This summary is machine-generated.

We introduce two novel models for scale-free networks with a degree distribution exponent of one. These local rewiring models exhibit disassortative correlations and degree-dependent clustering in finite networks.

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Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Scale-free networks are common, but many models have degree exponents > 2.
  • Real-world networks often exhibit heavier-tailed degree distributions than predicted by standard models.

Purpose of the Study:

  • To explore scale-free equilibrium network models with a degree distribution exponent of one (γ=1).
  • To investigate the properties of these models, particularly concerning degree-degree correlations and clustering, in finite-sized networks.

Main Methods:

  • Developed two local rewiring mechanisms for network generation.
  • Analyzed network properties in the infinite size limit and investigated finite size effects using simulations.

Main Results:

  • The models generate uncorrelated networks in the infinite size limit.
  • Finite-sized networks exhibit disassortative degree-degree correlations.
  • Observed markedly degree-dependent clustering in finite networks.

Conclusions:

  • The proposed models provide a framework for understanding scale-free networks with heavy-tailed degree distributions (γ=1).
  • Local rewiring mechanisms can lead to complex correlations and clustering phenomena in finite networks.
  • Identified a real-world network exhibiting a similar degree distribution.