When you sample from the posterior and take the vertex marginals, is it proper to say that we can interpret the marginals for a given vertex as being the degree of membership in the communities (fuzzy community membership)?

If so, how does this differ from the overlapping blockstate? I saw in the mailing list that overlapping is only supported at the base level:

But, even if it were supported at every level, what does this achieve that the fuzzy model averaging doesn't? Could you do model averaging with the overlapping state too? E.g., in sample 1 vertex A is in communities c1, c2. In sample 2 vertex A is in communities c1, c4. Etc. Would this be in some way a more accurate measure of multiple community membership than the fuzzy?

Thanks