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The plane-wave density functional theory code CASTEP was used with the Tkatchenko-Scheffler van der Waals correction scheme and the generalized gradient approximation of Perdew, Burke, and Emzerhof (GGA PBE) to calculate the binding energy of Au, Cr, and Al atoms on the armchair and zigzag edge binding sites of monolayer graphene, and at the high-symmetry adsorption sites of single layer, bilayer, and trilayer graphene. All edge site binding energies were found to be substantially higher than the adsorption energies for all metals. The adatom migration activation barriers for the lowest energy migration paths on pristine monolayer, bilayer, and trilayer graphene were then calculated and found to be smaller than or within an order of magnitude of kB T at room temperature, implying very high mobility for all adatoms studied. This suggests that metal atoms evaporated onto graphene samples quickly migrate across the lattice and bind to the energetically favorable edge sites before being characterized in the microscope. We then prove this notion for Al and Au on graphene with scanning transmission electron microscopy (STEM) images showing that these atoms are observed exclusively at edge sites, and also hydrocarbon-contaminated regions, where the pristine regions of the lattice are completely devoid of adatoms. Additionally, we review the issue of fixing selected atomic positions during geometry optimization calculations for graphene/adatom systems and suggest a guiding principle for future studies. [ABSTRACT FROM AUTHOR]