I think you are not really interested in the "communities" but just the dense subgraphs. As Tiago already very nicely explained, these two are quite different things. The existence of dense subgraphs might just be a result of statistical fluctuations in the underlying model or they may simply arise because of the particular form of a degree sequence. As he also warned, if you make a mistake of treating these as "real" communities in the underlying generative model, you may infer very wrong conclusions about the model that may not be valid about a different realization of the same model. On the other hand if you really care _only_ about a given realization, it is perhaps fine to ignore the underlying generative model. You might like to have a look at this which explains these things:

http://link.springer.com/article/10.1007/s41109-017-0023-6