We present a computational investigation of adsorption on graphene concerning the second-row diatomic molecules (Li2, B2, C2, O2, N2 and F2). The adsorption energies and the nature of the interaction between guest molecules and graphene, in both periodic and non-periodic approaches, were evaluated using dispersion-corrected density functional theory calculations (DFT/PBE-D3). A periodic graphene model, used to tune the coverage, is compared with a cluster model in which the graphene sheet is represented by coronene. The results of both energetic and electronic state analyses reveal a variety of adsorption processes. While B2 and C2 adsorb in a bridge position in order to establish two covalent bonds with the surface, O2 and N2 are clearly physisorbed in positions parallel to the surface. Li2 and F2 show intermediate behavior, with strong physisorption accompanied by charge transfer.