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Preferential attachment in growing spatial networks.

Luca Ferretti1, Michele Cortelezzi

  • 1Centre de Recerca en Agrigenòmica and Departament de Ciència Animal i dels Aliments, Universitat Autònoma de Barcelona, Bellaterra, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

We analyzed growing network models on curved spaces, finding their degree distributions resemble the Bianconi-Barabási fitness model. Curvature can lead to Bose-Einstein condensation, impacting network structure and link lengths.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Growing network models are crucial for understanding real-world systems.
  • Preferential attachment is a common mechanism in network evolution.
  • The Bianconi-Barabási fitness model describes heterogeneous network growth.

Purpose of the Study:

  • To derive the degree distribution for growing networks on curved spaces.
  • To investigate the role of space curvature and node distance in network formation.
  • To explore phenomena like Bose-Einstein condensation in these models.

Main Methods:

  • Developing growing network models with distance-weighted preferential attachment.
  • Analyzing degree distributions on spaces of constant curvature (spherical, flat, hyperbolic).
  • Investigating the influence of metric and node density on fitness distribution.

Main Results:

  • Degree distributions are similar to the Bianconi-Barabási fitness model.
  • Curvature singularities can induce asymptotic Bose-Einstein condensation.
  • Transient condensation is observed in strongly curved hyperbolic spaces.
  • Numerical results are provided for various constant curvature spaces.

Conclusions:

  • Network degree distributions are influenced by spatial geometry and attachment rules.
  • Bose-Einstein condensation is a potential emergent phenomenon in these growing networks.
  • Understanding attachment dynamics is key to predicting network properties and link length distributions.