  An important feature of many complex systems, both natural and artificial, is
the structure and organization of their interaction networks with interesting
properties. Here we present a theory of self-organization by evolutionary
adaptation in which we show how the structure and organization of a network is
related to the survival, or in general the performance, objectives of the
system. We propose that a complex system optimizes its network structure in
order to maximize its overall survival fitness which is composed of short-term
and long-term survival components. These in turn depend on three critical
measures of the network, namely, efficiency, robustness and cost, and the
environmental selection pressure. Using a graph theoretical case study, we show
that when efficiency is paramount the "Star" topology emerges and when
robustness is important the "Circle" topology is found. When efficiency and
robustness requirements are both important to varying degrees, other classes of
networks such as the "Hub" emerge. Our assumptions and results are consistent
with observations across a wide variety of applications.
