  While many large infrastructure networks, such as power, water, and natural
gas systems, have similar physical properties governing flows, these systems
tend to have distinctly different sizes and topological structures. This paper
seeks to understand how these different size-scales and topological features
can emerge from relatively simple design principles. Specifically, we seek to
describe the conditions under which it is optimal to build decentralized
network infrastructures, such as a microgrid, rather than centralized ones,
such as a large high-voltage power system. While our method is simple it is
useful in explaining why sometimes, but not always, it is economical to build
large, interconnected networks and in other cases it is preferable to use
smaller, distributed systems. The results indicate that there is not a single
set of infrastructure cost conditions under which optimally-designed networks
will have highly centralized architectures. Instead, as costs increase we find
that average network sizes increase gradually according to a power-law. When we
consider the reliability costs, however, we do observe a transition point at
which optimally designed networks become more centralized with larger
geographic scope. As the losses associated with node and edge failures become
more costly, this transition becomes more sudden.
