For single-atom catalysts (SACs), the dopants situated near the metal site have demonstrated a significant impact on the catalytic properties. However, the effect of dopants situated further away from the metal centers and their working mechanisms remain to be elucidated. Herein, we conduct density functional theory-driven studies on regulating the peripheral nitrogen dopants in graphene-based SACs, with a particular focus on Ir1 SAC, for propane dehydrogenation (PDH). It is found that increasing the distance between the N dopant and the Ir1 site results in a different energy change for the reaction process compared to the dense doping model with only first and second-shell N species. The proposed stochastic doping models demonstrate statistically that increasing the N dopant in farther shells not only enhances the activity of Ir1 but also maintains a high selectivity for propene, which is verified by experimental tests. The modulation of the d-band center of Ir1 by stochastic N dopants effectively modifies the binding strength of reaction intermediates, thereby enabling the optimization of the potential energy surface of PDH. These results deepen the understanding of dopant states around metal sites and provide an important implication for the doping engineering in heterogeneous catalysis.