bflat- There are two versions of Hughie Graham (Child #191) in DT. The one in file HUGRAME2 is from 'The Scots Musical Museum', #303. The story is that Robert Burns contributed this song without a tune to SMM. So far as is known (Bronson, 'The Traditional Tunes of the Child Ballads', #191) the coupling of it to the tune "Drimen Duff" (probably taken from Oswald's 'Caledonian Pocket Companion', book 8), was an arbitrary choice. As you will see from the notes with "Drumion Dubh" in the Scarce Songs 1 file on my website, this is the tune that Burke Thumoth published earlier as an Irish tune. This tune is not related to Leadbelly's.
There is also a different Scots tune called "Druimionn Dubh" in Corri's 'Scots Songs', 1783, and MacDonald's "Highland Airs', 1784. Burns wrote "Musing on the roaring ocean" to this latter tune (Scots Musical Museum, #179). [Corri's single verse is given on my website under "Drumion dubh".]