In this thesis, We investigate the effects of randomly distributed atomic defects on the magnetic and electronic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. We show that electron-electron interaction effects not only make defect states robust as compared with the tight-binding results,but also make edge states fragile even at low defect concentration for clean edge sites. For a balanced defect distribution among the sublattices of the honeycomb lattice in the bulk region of the ribbon, the ground state antiferromagnetism of the edge states remains unaffected. By analyzing the excitation spectrum, we show that while the antiferromagnetic ground state is susceptible to single spin flip excitations from edge states to magnetic defect states at low defect concentrations, it’s overall stability is enhanced with respect to the ferromagnetic phase. Then, we investigated Anderson localization induced metal to insulator transition by a localization length in nanometer scale up to 5% vacancy concentration by using time dependent results. We found that, Anderson localization is stronger at the vicinity of Fermi level energy states since those states are becoming full of impurity states and edge states, mixed.