Controlled covalent modification of graphene via electrochemically assisted grafting of molecules is expected to be a robust method for tuning the doping levels and work function and therefore enabling the deployment of graphene in photovoltaic and battery applications. By using aryliodonium salts, in particular, bis(4-nitrophenyl)iodonium tetrafluoroborate, the grafting density can be adjusted from 4 × 10(13) to 3 × 10(14) molecules per cm(2). New insights on the grafting mechanism and the reactivity of the graphene are reported here. Clean basal planes were found to have increased reactivity compared to atomic-level point defects (single vacancies). High resolution scanning tunnelling microscopy (STM) shows that some of the grafts present three-fold symmetry, which may indicate that the grafts are pairs of molecules. The point of attachment of the second molecule is under investigation using computational work which includes simulations of the STM images. Elongated as well as extended grafts (larger than 4 nm) are also observed.