Modeling the evolution of weighted networks

Alain Barrat, Marc Barthélemy, and Alessandro Vespignani
Phys. Rev. E 70, 066149 – Published 30 December 2004

Abstract

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges’ weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights’ reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a nontrivial time evolution of vertices’ properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices’ degree.

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  • Received 10 June 2004

DOI:https://doi.org/10.1103/PhysRevE.70.066149

©2004 American Physical Society

Authors & Affiliations

Alain Barrat1, Marc Barthélemy2, and Alessandro Vespignani1,3

  • 1Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210, Université de Paris–Sud, 91405 Orsay, France
  • 2Département de Physique Théorique et Appliquée, CEA–Centre d’Etudes de Bruyères-le-Châtel, Boîte Postale 12, 91680 Bruyères-Le-Châtel, France
  • 3School of Informatics, Indiana University, Bloomington, Indiana 47408, USA

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Issue

Vol. 70, Iss. 6 — December 2004

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