A family of small graphene patches, i.e., rectangular polyaromatic hydrocarbons (PAHs), that have both zigzag and armchair edges is investigated to establish their ground state electronic structure. Broken symmetry density functional theory (DFT) and plane wave DFT were used to characterize the onset of diradical character via relative energies of open-shell and closed-shell singlet states. The perfect pairing (PP) active space approximation of coupled cluster theory was used to characterize diradical character on the basis of promotion of electrons from occupied to unoccupied molecular orbitals. The role of zigzag and armchair edges in the formation of open-shell singlet states is elucidated. In particular, it is found that elongation of the zigzag edge results in an increase of diradical character whereas elongation of the arm chair edge leads to a decrease of diradical character. Analysis of orbitals from PP calculations suggests that diradical states are formally Mobius aromatic multiconfigurational systems.