In general, an AF-algebra can has some different Bratteli diagrams. We can add some identical arrows to make the Bratteli diagrams different, but it is too trivial, are any good examples?
For which AF-algebras, its Bratteli diagram can be unique decided? I think the UHF algebras should be. How about others?
A same question is at here: https://math.stackexchange.com/questions/654472/bratteli-diagram-decided-by-af-algebras