  Many complex systems can be described in terms of networks of interacting
units. Recent studies have shown that a wide class of both natural and
artificial nets display a surprisingly widespread feature: the presence of
highly heterogeneous distributions of links, providing an extraordinary source
of robustness against perturbations. Although most theories concerning the
origin of these topologies use growing graphs, here we show that a simple
optimization process can also account for the observed regularities displayed
by most complex nets. Using an evolutionary algorithm involving minimization of
link density and average distance, four major types of networks are
encountered: (a) sparse exponential-like networks, (b) sparse scale-free
networks, (c) star networks and (d) highly dense networks, apparently defining
three major phases. These constraints provide a new explanation for scaling of
exponent about -3. The evolutionary consequences of these results are outlined.
