Nanofluid is a new-concept solution wherein nm-sized solid particles of excellent, higher-than-base-fluid thermal conductivity are stably suspended. Recently, high-thermal-conductivity graphene nanoparticles have attracted particularly close attention from researchers. In the present study, the thermal conductivity and viscosity properties of three kinds of graphene nanofluid added to distilled water - two graphenes of differing size and oxidized graphene - were compared and analyzed. The thermal conductivities of the nanofluids, formulated in the usual manner by adding graphene to distilled water and subjecting the mixture to ultrasonic dispersion, were measured by the transient hot-wire method, and the viscosities were determined using a rotational digital viscometer. As a result, we concluded that the nanofluid of small average particle diameter and that which incorporates oxidized graphene have outstanding properties as heat transfer media, due to their excellent thermal conductivity and viscosity, compared with the other graphene nanofluids.