In my opinion it is not polymer - but this decision depents on understanding of the definition. Lets take graphite or diamond for help. Both have periodic infinite structures and are nonmolecular allotropes of carbon (and are not called polymers). There is no typical subunit (monomer - molecule) except of carbon atom as alone. So we do not have monomeric unit of macromolecule and therefore we should not speak about polymer (which means something like "mixture of macromolecules" - so, beside all, one layer of atoms is hard to clasify like "polymer" because it is one macromolecule maximally). Which leads us to the last point. The term "graphene" (strictly speaking monoatomic 2D structure - so something like general motive but with exact composition) is something on the border of usual and traditional chemical terminology and clasification (like molecule, macromolecule, chain or layer - which are general). And finally, graphene can not be chemical compound as it is a constituent of one type of atoms only. It can be clasified as carbon allotrop (or better say a 2D motive characteristic for some carbon allotropes). Conclusion: no polymer, no compound.

graphene is not a polymer. but it behaves like poly aromatic compounds

a 2Dimensional, Sp2 hybridized carbon arranged in the hexagonal  lattice

Thank you sir, Lukáš Richtera for this beautiful explanation

Graphene is not a polymer. However, it can be called polycarbon as each layer is build up of c atom interlinked to each other akin to a crosslinked polymer. For a polymer you have single unit called monomer. For graphene you can not identify a single unit. You can get graphene from polymer by heating at high temperature in inert atmosphere.

thank u sir