Somewhat, yes. It seems that graphite is a somewhat more relaxed state than carbon's diamond crystal allotrope.

Both burn, and can be vaporized with LOX/acetyline torches:

http://www.popsci.com/sites/popsci.com/files/styles/medium_1...

But apparently, over long periods of time, and unless coerced, carbon prefers to be graphite and so, diamonds can decay as such. [0]

[0] https://en.wikipedia.org/wiki/Material_properties_of_diamond...

Hence why graphite is generally more plentiful than diamonds.