  To analyze the transport of information or material from a source to every
node of a network we use two quantities introduced in the study of river
networks: the cost and the flow. For a network with $K$ nodes and $M$ levels,
we show that an upper bound to the global cost is $C_{0,max}\propto KM$. From
numerical simulations for spanning tree networks with scale-free topology and
with $10^2$ up to $10^7$ nodes, it is found, for large $K$, that the average
number of levels and the global cost are given by $M\propto \ln(K)$ and
$C_0\propto K\ln (K)$, respectively. These results agree very well with the
ones obtained from a mean-field approach. If the network is characterized by a
degree distribution of connectivity $P(k)\propto k^{- \gamma}$, we also find
that the transport efficiency increases as long as $\gamma$ decreases and that
spanning tree networks with scale-free topology are more optimized to transfer
information or material than random networks.
