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This paper investigates the potential of graphene nonreciprocal gyrotropy for microwave applications. First, the problem of a plane wave obliquely impinging on a graphene sheet is analyzed to provide physical insight into the fundamentals of graphene gyrotropy. It is found that graphene rotates the polarization of any plane wave impinging on it. The rotation angle is larger for H-polarized oblique waves than for normally incident waves and increases as the angle of incidence increases. The opposite holds for E waves. A general transmission matrix model is then developed for an arbitrary cylindrical waveguide and for a graphene sheet inside such a waveguide. This model is next applied to a circular cylindrical waveguide loaded with one or several graphene sheets and excited in its dominant H11 mode. Although the rotation angle from a single graphene sheet is quite high at high chemical potential, the corresponding transmission level is small due to the poor matching associated with the high density of the sheet. This fact prohibits the cascading of graphene sheets with high chemical potential as an approach to increase the amount of rotation. However, by decreasing the chemical potential, graphene may be well matched to waveguide modes, and therefore a large number of graphene sheets (ten in this study) may be used to produce a significant amount of rotation with relatively low insertion loss.