  Many complex natural and physical systems exhibit patterns of interconnection
that conform, approximately, to a network structure referred to as scale-free.
Preferential attachment is one of many algorithms that have been introduced to
model the growth and structure of scale-free networks. With so many different
models of scale-free networks it is unclear what properties of scale-free
networks are typical, and what properties are peculiarities of a particular
growth or construction process. We propose a simple maximum entropy process
which provides the best representation of what are typical properties of
scale-free networks, and provides a standard against which real and
algorithmically generated networks can be compared. As an example we consider
preferential attachment and find that this particular growth model does not
yield typical realizations of scale-free networks. In particular, the widely
discussed "fragility" of scale-free networks is actually found to be due to the
peculiar "hub-centric" structure of preferential attachment networks. We
provide a method to generate or remove this latent hub-centric bias --- thereby
demonstrating exactly which features of preferential attachment networks are
atypical of the broader class of scale-free networks. We are also able to
statistically demonstrate whether real networks are typical realizations of
scale-free networks, or networks with that particular degree distribution;
using a new surrogate generation method for complex networks, exactly analogous
the the widely used surrogate tests of nonlinear time series analysis.
