We propose an equivalent longitudinal circuit to characterize surface plasmon polaritons (SPPs) propagation along spatially dispersive graphene parallel plate waveguides. This circuit allows the fast analysis of the propagating modes, taking into account the spatially dispersive nature of graphene's conductivity and providing physical insight into the propagation mechanisms. Importantly, the influence of spatial dispersion can be elegantly absorbed by a per-unit length shunt capacitance proportional to the intrinsic surface quantum capacitance of graphene. The precision and limitations of this circuit are analyzed in detail. Finally, the impact of spatial dispersion in the performance of graphene-based devices is discussed. Numerical simulations confirm that this phenomenon can significantly modify the expected response of the devices. However, such influence can easily be compensated by rigorously taking into account spatial dispersion at the device design stage.