  There is a pressing need for a description of complex systems that includes
considerations of the underlying network of interactions, for a diverse range
of biological, technological and other networks. In this work relationships
between second-order phase transitions and the power laws associated with
scale-free networks are directly quantified. A unique unbiased partitioning of
complex networks (exemplified in this work by software architectures) into
high- and low-connectivity regions can be made. Other applications to finance
and aerogels are outlined.
