Understanding the catalytic performance of different materials is of crucial importance for achieving further technological advancements. This especially relates to the behaviors of different classes of catalysts under operating conditions. Here, we analyzed the effects of local coordination of metal centers (Mn, Fe, Co) in graphene-embedded single-atom catalysts (SACs). We started with well-known M@N-4-graphene catalysts and systematically replaced nitrogen atoms with oxygen or sulfur atoms to obtain M@OxNy-graphene and M@SxNy-graphene SACs (x + y = 4). We show that local coordination strongly affects the electronic structure and reactivity towards hydrogen and oxygen species. However, stability is even more affected. Using the concept of Pourbaix plots, we show that the replacement of nitrogen atoms in metal coordinating centers with O or S destabilized the SACs towards dissolution, while the metal centers were easily covered by O and OH, acting as additional ligands at high anodic potentials and high pH values. Thus, not only should local coordination be considered in terms of the activity of SACs, but it is also necessary to consider its effects on the speciation of SAC active centers under different potentials and pH conditions.