thanks, this is already quite helpful. Short follow-up:

Our final aim is to sample from the fitted model, also according to the inferred edge covariate distributions between groups. Is this somehow possible with graph-tool? (Up to now we were not able to do this.)

Would it, in any case, be valid to retrieve the empirical distributions between each group from the fitted model and to fit a non-microcanonical version of the distributions (like binomial) to the covariates for each group combination, which could then be used to sample a weighted SBM e.g. with graspy? Or do you see a more direct way?

thanks, this is already quite helpful. Short follow-up:

Our final aim is to sample from the fitted model, also according to the inferred edge covariate distributions between groups. Is this somehow possible with graph-tool? (Up to now we were not able to do this.)

Not directly, currently graph-tool does not have a function to sample
from the weighted SBM.

If you open a ticket in the website with the feature requiest, I will
implement this when I find the time.

Would it, in any case, be valid to retrieve the empirical distributions between each group from the fitted model and to fit a non-microcanonical version of the distributions (like binomial) to the covariates for each group combination, which could then be used to sample a weighted SBM e.g. with graspy? Or do you see a more direct way?

It would be valid as a reasonable approximation, since the models become
equivalent as the number of edges becomes sufficiently large.