  The small-world property is known to have a profound effect on the navigation
efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)].
Accordingly, the proper addition of shortcuts to a regular substrate can lead
to the formation of a highly efficient structure for information propagation.
Here we show that enhanced flow properties can also be observed in these
complex topologies. Precisely, our model is a network built from an underlying
regular lattice over which long-range connections are randomly added according
to the probability, $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is the
Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a
controlling parameter. The mean two-point global conductance of the system is
computed by considering that each link has a local conductance given by
$g_{ij}\propto r_{ij}^{-\delta}$, where $\delta$ determines the extent of the
geographical limitations (costs) on the long-range connections. Our results
show that the best flow conditions are obtained for $\delta=0$ with $\alpha=0$,
while for $\delta \gg 1$ the overall conductance always increases with
$\alpha$. For $\delta\approx 1$, $\alpha=d$ becomes the optimal exponent, where
$d$ is the topological dimension of the substrate. Interestingly, this exponent
is identical to the one obtained for optimal navigation in small-world networks
using decentralized algorithms.
