  We study the optimal distance in networks, $\ell_{\scriptsize opt}$, defined
as the length of the path minimizing the total weight, in the presence of
disorder. Disorder is introduced by assigning random weights to the links or
nodes. For strong disorder, where the maximal weight along the path dominates
the sum, we find that $\ell_{\scriptsize opt}\sim N^{1/3}$ in both
Erd\H{o}s-R\'enyi (ER) and Watts-Strogatz (WS) networks. For scale free (SF)
networks, with degree distribution $P(k) \sim k^{-\lambda}$, we find that
$\ell_{\scriptsize opt}$ scales as $N^{(\lambda - 3)/(\lambda - 1)}$ for
$3<\lambda<4$ and as $N^{1/3}$ for $\lambda\geq 4$. Thus, for these networks,
the small-world nature is destroyed. For $2 < \lambda < 3$, our numerical
results suggest that $\ell_{\scriptsize opt}$ scales as $\ln^{\lambda-1}N$. We
also find numerically that for weak disorder $\ell_{\scriptsize opt}\sim\ln N$
for both the ER and WS models as well as for SF networks.
