Maximum Entropy Distributions with Applications to Graph Simulation

The problem of simulating graphs (networks) subject to constraints has been studied extensively across several areas. Applications of this problem include modeling inter-bank financial networks, predator-prey ecological graphs, contingency tables, and even studying larger networks such as the Internet. In “Maximum Entropy Distributions with Applications to Graph Simulation,” P. Glasserman and E. Lelo de Larrea study the more general problem of sampling uniformly from product sets under linear constraints, which includes simulating bipartite, directed, and undirected graphs with given degree sequences. For this purpose, they consider two suitable probability distributions: one that maximizes the entropy of the system, and another that maximizes the minimum probability of hitting the desired target set. Although apparently different, the authors provide conditions under which both distributions coincide. In addition, they propose a simple sequential algorithm to sample medium-sized graphs with fixed degrees.