  The exponential family of random graphs is among the most widely-studied
network models. We show that any exponential random graph model may
alternatively be viewed as a lattice gas model with a finite Banach space norm.
The system may then be treated by cluster expansion methods from statistical
mechanics. In particular, we derive a convergent power series expansion for the
limiting free energy in the case of small parameters. Since the free energy is
the generating function for the expectations of other random variables, this
characterizes the structure and behavior of the limiting network in this
parameter region.
