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- W2018068632 abstract "When transport in networks follows the shortest paths, the link weights are shown to play a crucial role. If the underlying topology with $N$ nodes is not changed and if the link weights are independent from each other, then we show that, by tuning the link weights, a phase transition occurs around a critical extreme value index ${ensuremath{alpha}}_{c}$ of the link weight distribution. If the extreme value index of the link weight distribution $ensuremath{alpha}>{ensuremath{alpha}}_{c}$, transport in the network traverses many links whereas for $ensuremath{alpha}<{ensuremath{alpha}}_{c}$, all transport flows over a critical backbone consisting of $Nensuremath{-}1$ links. For connected Erdos-R'enyi random graphs ${G}_{p}(N)$ and square lattices, we have characterised the phase transition and found that ${ensuremath{alpha}}_{c}ensuremath{simeq}b{N}^{ensuremath{-}ensuremath{beta}}$ with ${ensuremath{beta}}_{{G}_{p}(N)}ensuremath{approx}0.63$ and ${ensuremath{beta}}_{text{lattice}}ensuremath{approx}0.62$." @default.
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- W2018068632 date "2005-11-30" @default.
- W2018068632 modified "2023-09-24" @default.
- W2018068632 title "Phase transition in the link weight structure of networks" @default.
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- W2018068632 doi "https://doi.org/10.1103/physreve.72.056138" @default.
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