A theoretical study using density functional theory was employed to analyze the hydrogen adsorption on Rh-2 and Ti-2 dimers decorating pyridine and pyrrolic-like nitrogen doped graphene. First, an analysis of geometry, stability, projected density of states, overlap population and charge distribution was performed to understand the interaction between Rh and Ti metal adatoms and dimers with pyridinic and pyrrolic graphene. Charge transfer occurs from metal to substrate in all cases. An investigation of H-2 adsorption on Rh and Ti metals dimers on pyridinic and pyrrolic N-doped graphene was also performed. Molecular adsorption states were observed for Ti on pyridinic graphene and for Rh on both substrates. H-2 dissociative adsorption occurs on both metal supported dimers. H(2)s states hybridize with the Rh and Ti d band, forming localized and dispersed states in concordance with the mechanisms observed for H-2 adsorption. The activation energies were calculated obtaining values smaller than 0.59 eV, indicating that the dissociation of H-2 can occur spontaneously at room temperature. HSE06 hybrid functional was used to test the accuracy of PBE-D2 functional in the activation energy calculation. Adsorption in the molecular states occurs with no barriers.