  Previous Raman measurements on supported graphene under high pressure
reported a very different shift rate of in-plane phonon frequency of graphene
(16 cm$^{-1}$GPa$^{-1}$) from graphite (4.7 cm$^{-1}$GPa$^{-1}$), implying very
different in-plane anharmonicity that graphene gets stiffer than graphite
in-plane under the same pressure. It was suggested that it could be due to the
adhesion of graphene to substrates. We have therefore performed high pressure
Raman measurements on unsupported graphene and we find a similar in-plane
stiffness and anharmonicity of graphene (5.4 cm$^{-1}$GPa$^{-1}$) to graphite.
On the other hand, the out-of-plane stiffness of graphene is hard to define,
due to the 2D nature of graphene. However, we estimate a similar out-of-plane
stiffness of graphene (1.4$\pm$295 GPa) to that of graphite (38.7$\pm$7 GPa),
by measuring its effect on the shift of the in-plane phonon frequency with
pressure.
