In this work, for the first time the electromagnetic features of graphene are characterized by a circuit model derived instead of fitted from the electric field integral equation (EFIE). The atomically thick graphene is equivalently replaced by an impedance surface. When it is magnetized, the impedance surface is anisotropic with a tensor conductivity. Based on EFIE, the graphene's circuit model can be derived by the partial element equivalency circuit (PEEC) concept. The anisotropic resistivity is modeled using a serial resistor with current control voltage sources (CCVSs). From the derived circuit model, electromagnetic properties of graphene can be conveniently analyzed. This work also provides a new characterization method for dispersive and anisotropic materials.