  Probabilistic generative models of graphs are important tools that enable
representation and sampling. Many recent works have created probabilistic
models of graphs that are capable of representing not only entity interactions
but also their attributes. However, given a generative model of random
attributed graph(s), the general conditions that establish goodness of fit are
not clear a-priori. In this paper, we define goodness of fit in terms of the
mean square contingency coefficient for random binary networks. For this
statistic, we outline a procedure for assessing the quality of the structure of
a learned attributed graph by ensuring that the discrepancy of the mean square
contingency coefficient (constant, or random) is minimal with high probability.
We apply these criteria to verify the representation capability of a
probabilistic generative model for various popular types of graph models.
