Graver basis for an undirected graph and its application to testing the   beta model of random graphs
  In this paper we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method. 
Mitsunori Ogawa, Hisayuki Hara, Akimichi Takemura
math.ST math.CO stat.TH