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- W2243812332 abstract "We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path ,opt in a disordered Erdős-Renyi (ER) random network and scale-free (SF) network. Each link i is associated with a weight ti ; expsarid, 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 finitea, there is a crossover network size N* sad at which the transition occurs. For N! N* sad the scaling behavior of ,opt is in the strong disorder regime, with ,opt, N 1/3 for ER networks and for SF networks with lo 4, and ,opt , N sl˛3d/sl˛1d for SF networks with 3 ,l, 4. For N@ N* sad the scaling behavior is in the weak disorder regime, with ,opt, ln N for ER networks and SF networks with l. 3. In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between N* sad and a. We find thatN* sa d, a 3 for ER networks and for SF networks with lo 4, and N* sa d, a sl˛1d/sl˛3d for SF networks with 3 ,l, 4." @default.
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- W2243812332 date "2005-03-21" @default.
- W2243812332 modified "2023-09-23" @default.
- W2243812332 title "Effect of Disorder Strength on Optimal Paths in Complex Networks" @default.
- W2243812332 hasPublicationYear "2005" @default.
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