Universal behavior of optimal paths in weighted networks with general disorder

Abstract

We study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter ($S\equiv A{L}^{-1/\nu }$ for $d$-dimensional lattices, and $S\equiv A{N}^{-1/3}$ for random networks) determines the distributions of the optimal path length, including both strong and weak disorder regimes. Here $\nu$ is the percolation connectivity exponent, and $A$ depends on the percolation threshold and $P(w)$. For $P(w)$ uniform, Poisson or Gaussian the crossover from weak to strong does not occur, and only weak disorder exists.

Accepted by PRL

References in corpus (4)

• Optimal Paths in Disordered Complex Networks
• Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder
• Effect of Disorder Strength on Optimal Paths in Complex Networks
• Phase Diagram of Optimal Paths

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