Universal behavior of optimal paths in weighted networks with general disorder

Details Universal behavior of optimal paths in weighted networks with general disorder Universal behavior of optimal paths in weighted networks with general disorder

2005-08-31

arxiv.org/abs/cond-mat/0508759v2

Phys.Rev.Lett., 96, 068702(2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Accepted by PRL

Scientific paper

10.1103/PhysRevLett.96.068702

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 ($S \equiv AL^{-1/\nu}$ for $d$-dimensional lattices, and $S\equiv AN^{-1/3}$ 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.

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