Chemical reactions that convert sp2 to sp3 hybridization have been demonstrated to be a fascinating yet challenging route to functionalize graphene. So far it has not been possible to precisely control the reaction sites nor their lateral order at the atomic/molecular scale. The application prospects have been limited for reactions that require long soaking, heating, electric pulses or probe-tip press. Here we demonstrate a spatially selective photocycloaddition reaction of a two-dimensional molecular network with defect-free basal plane of single-layer graphene. Directly visualized at the submolecular level, the cycloaddition is triggered by ultraviolet irradiation in ultrahigh vacuum, requiring no aid of the graphene Moiré pattern. The reaction involves both [2+2] and [2+4] cycloadditions, with the reaction sites aligned into a two-dimensional extended and well-ordered array, inducing a bandgap for the reacted graphene layer. This work provides a solid base for designing and engineering graphene-based optoelectronic and microelectronic devices.