  We present an analysis of the classical contact process on scale-free
networks. A mean-field study, both for finite and infinite network sizes,
yields an absorbing-state phase transition at a finite critical value of the
control parameter, characterized by a set of exponents depending on the network
structure. Since finite size effects are large and the infinite network limit
cannot be reached in practice, a numerical study of the transition requires the
application of finite size scaling theory. Contrary to other critical phenomena
studied previously, the contact process in scale-free networks exhibits a
non-trivial critical behavior that cannot be quantitatively accounted for by
mean-field theory.
