Traditionally, Organic materials defined as living organism, mostly containing C-H bonds. But later on many non-living materials included in the organic compounds containing C-H bonds. Most are combinations of a few of the lightest elements, particularly hydrogen, carbon, nitrogen, and oxygen.
On the other hand, An inorganic compound is typically lacks C-H bonds. Mostly consist of heavy elements in the periodic table.
In that sense, Graphene may be categorized as organic materials.
Though this question is interesting... the answers are always confusing. Yesterday, on Quora, I have received an answer saying graphene is inorganic. (https://www.quora.com/Is-graphene-an-organic-or-an-inorganic-material)
It seems like there are wide disagreements in this aspect... some call grapehene inorganic, some call it organic.