We report investigation of the geometry and electronic structure of iridium atoms adsorbed onto graphene through a combined experimental and theoretical study. Ir atoms were deposited onto a flake of graphene on a Pt(111) surface and found to form clusters even at low temperatures. The areal density of the observed clusters on the graphene flake suggests the clusters are most likely pairs of Ir atoms. Theoretical ab initio density functional (DFT) calculations indicate that these Ir dimers are oriented horizontally, near neighboring "bridge" sites of the graphene lattice, as this configuration has the strongest adsorption energy of all high-symmetry configurations for the Ir dimer. A large peak in the local density of states (LDOS) at the Dirac point energy was measured via scanning tunneling spectroscopy, and this result is reproduced by a DFT calculation of the LDOS. The peak at the Dirac point energy is found to be from the Ir s and p states. The LDOS in the monomer case was also calculated, and is found to significantly differ from the experimentally determined data, further supporting the hypothesis of low-temperature clustering