We review the analysis of the length of the optimal path ℓopt in random networks with disorder (i.e., random weights on the links). In the case of strong disorder, in which the maximal weight along the path dominates the sum, we find that ℓopt increases dramatically compared to the known...

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...

We study the optimal distance ℓopt in random networks in the presence of disorder implemented by assigning random weights to the links. The optimal distance between two nodes is the length of the path for which the sum of weights along the path (“cost”) is a minimum. We study the case of...