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Transition between strong and weak disorder regimes for the optimal path

Author

Listed:
  • Sreenivasan, Sameet
  • Kalisky, Tomer
  • Braunstein, Lidia A.
  • Buldyrev, Sergey V.
  • Havlin, Shlomo
  • Eugene Stanley, H.

Abstract

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ℓopt in a disordered Erdős–Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight τi≡exp(ari), where ri is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a, there is a crossover network size N*(a) such that for N⪡N*(a) the scaling behavior of ℓopt is in the strong disorder regime, while for N⪢N*(a) the scaling behavior is in the weak disorder regime. We derive the scaling relation between N*(a) and a with the help of simulations and also present an analytic derivation of the relation.

Suggested Citation

  • Sreenivasan, Sameet & Kalisky, Tomer & Braunstein, Lidia A. & Buldyrev, Sergey V. & Havlin, Shlomo & Eugene Stanley, H., 2005. "Transition between strong and weak disorder regimes for the optimal path," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 174-182.
    • Handle: RePEc:eee:phsmap:v:346:y:2005:i:1:p:174-182
    DOI: 10.1016/j.physa.2004.08.064
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