The cycloaddition reactions and noncovalent pi interactions of 2,3-dimethoxybutadiene (DMBD), 9-methylanthracene (MeA), tetracyanoethylene (TCNE), and maleic anhydride (MA) with graphene models have been investigated using density functional theory (DFT) calculations. Reaction enthalpies have been obtained to assess the reactivity and selectivity of covalent and noncovalent functionalization. Results indicate that graphene edges may be functionalized by the four reagents through cycloaddition reactions, while the interior regions cannot react. Noncovalent complexation is much more favorable than cycloaddition reactions on interior bonds of graphene. The relative reactivities of different sites in graphene are related to loss of aromaticity and can be predicted using Huckel molecular orbital (HMO) localization energy calculations.