Validity of graph-based molecular representation in ML

I was reading about molecular graph based generative models, which attempt to generate new molecules by training on a subset of a molecular dataset, such as QM9. In these works, there are 2 types of constraints that define the validity of the output:


1. The sum of the order of the bonds that are incident to an atom may
not exceed its valency.
2. The output should be a single connected graph.


While we can go further and do DFT calculations to see if these are also stable structures, I was wondering if there are any other simple constraints that we can impose to check the validity of the output molecular graph, without the need for DFT-type calculations.


