  We study the transport properties of model networks such as scale-free and
Erd\H{o}s-R\'{e}nyi networks as well as a real network. We consider the
conductance $G$ between two arbitrarily chosen nodes where each link has the
same unit resistance. Our theoretical analysis for scale-free networks predicts
a broad range of values of $G$, with a power-law tail distribution $\Phi_{\rm
SF}(G)\sim G^{-g_G}$, where $g_G=2\lambda -1$, and $\lambda$ is the decay
exponent for the scale-free network degree distribution. We confirm our
predictions by large scale simulations. The power-law tail in $\Phi_{\rm
SF}(G)$ leads to large values of $G$, thereby significantly improving the
transport in scale-free networks, compared to Erd\H{o}s-R\'{e}nyi networks
where the tail of the conductivity distribution decays exponentially. We
develop a simple physical picture of the transport to account for the results.
We study another model for transport, the \emph{max-flow} model, where
conductance is defined as the number of link-independent paths between the two
nodes, and find that a similar picture holds. The effects of distance on the
value of conductance are considered for both models, and some differences
emerge. We then extend our study to the case of multiple sources, where the
transport is define between two \emph{groups} of nodes. We find a fundamental
difference between the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an optimal number of
sources, or users, for the max-flow case. A qualitative (and partially
quantitative) explanation is also given.
