The effects of spin contamination on the stability and the spin densities of a model of graphene in the Hartree-Fock wavefunction (HF), Møller-Plesset perturbation theory (second order, MP2 and fourth order, MP4) and density functional theory (B3LYP and PBEPBE) are reported. It was found that the Hartree-Fock and MP2 wavefunctions of graphene suffer from the contamination from higher spin states and spin projection method failed to project out the spin contaminants. The spin density from HF was overestimated, while for MP2 it has the wrong trend. B3LYP and PBEPBE wavefunctions however have negligible contamination for higher spin states. Comparison with reported results showed that the spin densities at the center of the molecule from the pure functionals of PBEPBE were underestimated. Based on the comparison made, it was concluded that among the methods considered, the suitable one for use in the calculations of pristine graphene was B3LYP.