Abstract
The exponential family of random graphs are among the most widely studied networkmodels. We show that any exponential random graph model may alternatively be viewed asa lattice gas model with a finite Banach space norm. The system may then be treated usingcluster expansion methods from statistical mechanics. In particular, we derive a convergentpower series expansion for the limiting free energy in the case of small parameters. Sincethe 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 parameterregion.
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