Lithium Related Media Articles, page-22046

Graphite is a mineral. Elements are those in the periodic table, no more. Carbon is the element (Z = 6) and graphite is a mineral with 100 % carbon.

From Wikipedia: a mineral or mineral species is, broadly speaking, a solid substance with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.

Graphite is a solid substance with a well-defined chemical composition (carbon) and a specific crystal structure. Another mineral that shares the chemical composition of graphite (100 % carbon) but has different crystal structure is diamond. Last century, a new crystallographic structure was discovered for carbon: fullerene. However, it is not considered a mineral but a molecule. The reason for fullerenes not to be considered minerals is that they cannot growth while maintaining the same structure/spatial simmetry.
Finally we have welcome graphene this century, which basically is two-dimensional graphite, not a new mineral.

Carbon is the chemical element. Graphite and diamond are the two known minerals composed of 100 % carbon (they have different crystal structures). And fullerenes and graphene are different structures of carbon, but they are not new minerals.