Single atom catalysts (SACs) present the ultimate level of catalyst utilization, which puts them in the focus of current research. For this reason, their understanding is crucial for the development of new efficient catalytic systems. Using Density Functional Theory calculations, model SACs consisted of nine metals (Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt and Au) on four different supports (pristine graphene, N- and B-doped graphene and graphene with single vacancy) were analyzed. Among them, only graphene with a single vacancy enables the formation of SACs, which are stable in terms of aggregation and dissolution under harsh conditions of electrocatalysis. Reactivity of models SACs was probed using atomic (hydrogen and A = C, N, O and S) and molecular adsorbates (AHx, x = 1, 2, 3 or 4, depending on A), giving nearly 600 different systems included in this study. Scaling relations between adsorption energies of A and AHx on model SACs were confirmed. However, the scaling is broken for the case of CH3. There is also an evident scaling between adsorption energies of atomic and molecular adsorbates on metals SAs supported by pristine, N-doped and B-doped graphene, which originates from similar electronic structures of SAs on these supports. Using the obtained data, we have analyzed the hydrogen evolution on the model SACs. Only M@graphene vacancy systems (excluding Ag and Au) are stable under hydrogen evolution conditions in highly acidic solutions. Additional interfacial effects are discussed and the need for proper theoretical treatment when studying SACs interactions with molecular species.