Transition between strong and weak disorder regimes for the optimal path

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

Physica A: Statistical Mechanics and its Applications, 2005, vol. 346, issue 1, 174-182

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.

Keywords: Networks; Optimal path; Strong disorder (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:346:y:2005:i:1:p:174-182

DOI: 10.1016/j.physa.2004.08.064

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