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We study the incomplete oxidation of graphene or reduction of graphene oxide for hydroxyl and epoxy oxidant groups. While in wet oxidation hydroxyl groups are favorable, in a drier environment an oxygen atom can bridge two neighboring carbon atoms. We model composition variations and structural disorder within a statistical theory, the generalized quasichemical approximation, combined with density functional theory calculations of the local atomic geometries. A generalization of the statistical approach is developed to account for the antiparallel orientation of hydroxyl groups and a fourfold coordination of C atoms. The theoretical framework enables a thermodynamic treatment of graphene oxide as a function of oxygen content, allowing us to derive temperature-composition phase diagrams and investigate possible clustering and segregation. The resulting geometries, local and average electronic structures, and optical absorption spectra are discussed and compared with available experimental data.