1208.2992 (Mei Yin)

Critical phenomena in exponential random graphs    [PDF]

Mei Yin

The exponential family of random graphs is among the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, in imitation of the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one could analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating function for the limiting expectations of all thermodynamic observables. We derive the full phase diagram for a large family of 3-parameter exponential random graph models with attraction and show that they all consist of a first order surface phase transition bordered by a second order critical curve.

View original: http://arxiv.org/abs/1208.2992