Many-body wavefunctions were utilized to calculate von Neumann's entropy as an entanglement measurement for neutral and negatively charged nitrogen vacancy (NV) centers in diamond. A generalized Hubbard Hamiltonian which considers e-e interaction terms completely was used to calculate many-electron wavefunctions of the ground and excited states. Correlation between entanglement and spin density distributed on neighboring atoms of NV is presented. The behavior of spin density and entanglement under relaxations of neighboring atoms is the same for all investigated ground and excited states. The results suggest that the spin density may be used to quantify the entanglemnt and vice versa.