  We present an analysis of the topologies of a class of networks which are
optimal in terms of the requirements of having as short a route as possible
between any two nodes while yet keeping the congestion in the network as low as
possible. Strikingly, we find a variety of distinct topologies and novel phase
transitions between them on varying the number of links per node. Our results
suggest that the emergence of the topologies observed in nature may arise both
from growth mechanisms and the interplay of dynamical mechanisms with a
selection process.
