ApJ, in press

Abstract We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l opt in a disordered Erdős–Renyi (ER) random network and scale-free (SF) network. Each link i is associated with a weight τ i ≡ exp ( ar i ) , where r i 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 l opt 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.

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