The correlation of odd electrons in graphene turns out to be significant so that the species should be attributed to correlated ones. This finding profoundly influences the computational strategy addressing it to multireference computational schemes. Owing to serious problems related to the schemes realization, a compromise can be suggested using single-determinant approaches based on either Hartree-Fock or density-functional theory in the form of unrestricted open-shell presentation. Both computational schemes enable to fix the electron correlation, whereas only the Hartree-Fock theory suggests a set of quantities to be calculated that can quantitatively characterize the electron correlation and be used for a quantitative description of such graphene properties as magnetism, chemical reactivity, and mechanical response. The article presents concepts and algorithms of the unrestricted Hartree-Fock theory applied for the consideration of magnetic properties of nanographenes, their chemical modification by the example of stepwise hydrogenation, as well as a possible governing the electron correlation by the carbon skeleton deformation. © 2012 Wiley Periodicals, Inc.