Thank you very much for your detailed answer, it has been really helpful.
The point is that I want to know how the relations are beween the two types of nodes of my network and with both classifications. Other algorithms, such as map equation, classify both types of nodes in the same groups so I see this relations directly, althought as you say by this way some information is hidden. In this sense I prefer graphtool, but I didn't know how to get this relation.
Now I see I can get the partitions network from the BlockState object, I didn't know! (as I said, I am new in this, and in python too). I think it will be enough with this output.
Thank you again,
Andrea