Testing goodness-of-fit of random graph models

Random graphs are matrices with independent 0, 1 elements with probabilities determined by a small number of parameters. One of the oldest model is the Rasch model where the odds are ratios of positive numbers scaling the rows and columns. Later Persi Diaconis with his coworkers rediscovered the model for symmetric matrices and called the model beta. Here we give goodnes-of-fit tests for the model and extend the model to a version of the block model introduced by Holland, Laskey, and Leinhard.