  We introduce evolving networks where new vertices preferentially connect to
the more central parts of a network. This makes such networks compact. Finite
networks grown under the preferential compactness mechanism have complex
architectures, but infinite ones tend towards the opposite, having rapidly
decreasing distributions of connections. We present an analytical solution of
the problem for tree-like networks. Our approach links a collective
self-optimization mechanism of the emergence of complex network architectures
to self-organization mechanisms.
