We analyze the structural and electronic properties of graphene with high density monovacancies by first-principles and cluster expansion calculations in order to establish fundamental insights into the interaction between monovacancies in such conditions. The highest possible defect density is observed to exceed 7.1 atom% and, on the other hand, is bounded by 12.5 atom%. We demonstrate that the structural stability is controlled by the density of dangling bonds within a structure, for which we apply density functional tight bonding molecular dynamics calculations. Cluster expansion calculations are employed to determine the ground state structures as a function of the defect density. We observe a tendency of the monovacancies to form lines. Band structures and densities of states are calculated to evaluate the electronic properties. We find that the band dispersions around the Fermi energy are enhanced for increasing defect density, which indicates that the carrier mobility can be well controlled by means of this parameter.