  In this paper we consider spatial networks that realize a balance between an
infrastructure cost (the cost of wire needed to connect the network in space)
and communication efficiency, measured by average shortest pathlength. A global
optimization procedure yields network topologies in which this balance is
optimized. These are compared with network topologies generated by a
competitive process in which each node strives to optimize its own
cost-communication balance. Three phases are observed in globally optimal
configurations for different cost-communication trade-offs: (i) regular small
worlds, (ii) star-like networks and (iii) trees with a centre of interconnected
hubs. In the latter regime, i.e. for very expensive wire, power laws in the
link length distributions $P(w)\propto w^{-\alpha}$ are found, which can be
explained by a hierarchical organization of the networks. In contrast, in the
local optimization process the presence of sharp transitions between different
network regimes depends on the dimension of the underlying space. Whereas for
$d=\infty$ sharp transitions between fully connected networks, regular small
worlds and highly cliquish periphery-core networks are found, for $d=1$ sharp
transitions are absent and the power law behaviour in the link length
distribution persists over a much wider range of link cost parameters. The
measured power law exponents are in agreement with the hypothesis that the
locally optimized networks consist of multiple overlapping sub-optimal
hierarchical trees.
