Before revision:  We confirm some , but not all, prior results as to motif significance in these data sets. Code and datasets are freely available at URL
After revision:  We confirm some , but not in a yeast regulatory network. We also confirm using this method previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features. Conclusion: ERGMs allow the over- or under-representation of multiple non-independent structural configurations to be tested simultaneously in a single model. This can overcome some of the problems recently identified in mainstream methods for motif identification, specifically assumptions of normally distributed motif frequencies and independence of motifs.