Article abstract

Nature Physics 3, 813 - 817 (2007)
Published online: 30 September 2007 | doi:10.1038/nphys729

Subject Category: Statistical physics, thermodynamics and nonlinear dynamics

Self-organized network evolution coupled to extremal dynamics

Diego Garlaschelli1, Andrea Capocci2,3 & Guido Caldarelli2,4,5

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak–Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a 'fitness', and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.

  1. Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100 Siena, Italy
  2. Centro Studi e Ricerche e Museo della Fisica, 'E. Fermi', Compendio Viminale, 00184 Roma, Italy
  3. Dipartimento di Informatica e Sistemistica, via Salaria 113, 00185 Roma, Italy
  4. CNR-INFM Centro SMC, Dipartimento di Fisica, Università 'La Sapienza', Piazzale A. Moro 5, 00185 Roma, Italy
  5. Linkalab, Center for the Study of Complex Networks, 09100 Cagliari, Sardegna, Italy

Correspondence to: Guido Caldarelli2,4,5 e-mail: