  The structure of networks that provide optimal transport properties has been
investigated in a variety of contexts. While many different formulations of
this problem have been considered, it is recurrently found that optimal
networks are trees. It is shown here that this result is contingent on the
assumption of a stationary flow through the network. When time variations or
fluctuations are allowed for, a different class of optimal structures is found,
which share the hierarchical organization of trees yet contain loops. The
transitions between different network topologies as the parameters of the
problem vary are examined. These results may have strong implications for the
structure and formation of natural networks, as is illustrated by the example
of leaf venation networks.
