A cluster expansion approach to exponential random graph models

Details A cluster expansion approach to exponential random graph models A cluster expansion approach to exponential random graph models

2012-02-24

arxiv.org/abs/1202.5587v2

Physics

Mathematical Physics

13 pages, 1 figure

Scientific paper

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.

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