How does Metis treat the intermediate coarsened graphs?

Hi,I'd like to ask something about the way metis is coded.
From your papers we know that it would take several iterations until we reach the coarsest graph.
(G0 -> G1 -> G2 ... -> Gm)
During this period, Are the intermediate graphs(G1,G2...Gm-1,Gm) saved separately from G0?
Or do you replace (the nodes in a match) with a supernode?
Does the question's answer goes both for Metis and ParMetis?