  Graph generative models are a highly active branch of machine learning. Given
the steady development of new models of ever-increasing complexity, it is
necessary to provide a principled way to evaluate and compare them. In this
paper, we enumerate the desirable criteria for such a comparison metric and
provide an overview of the status quo of graph generative model comparison in
use today, which predominantly relies on the maximum mean discrepancy (MMD). We
perform a systematic evaluation of MMD in the context of graph generative model
comparison, highlighting some of the challenges and pitfalls researchers
inadvertently may encounter. After conducting a thorough analysis of the
behaviour of MMD on synthetically-generated perturbed graphs as well as on
recently-proposed graph generative models, we are able to provide a suitable
procedure to mitigate these challenges and pitfalls. We aggregate our findings
into a list of practical recommendations for researchers to use when evaluating
graph generative models.
