1202.5587 (Mei Yin)

A cluster expansion approach to exponential random graph models    [PDF]

Mei Yin

The exponential family of random graphs is among the most widely-studied of network models. A host of analytical and numerical techniques have been developed in the past. We show that any exponential random graph model could be alternatively viewed as a lattice gas model with a finite Banach space norm. The system could then be treated by cluster expansion methods in statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. This helps to give a complete characterization of the structure and behavior of the limiting network as the free energy is a generating function for the expectation values of all other observables.

View original: http://arxiv.org/abs/1202.5587