  By means of the ultrafast optical Kerr effect method coupled to optical
heterodyne detection (OHD-OKE), we characterize the third order nonlinear
response of graphene at telecom wavelength, and compare it to experimental
values obtained by the Z-scan method on the same samples. From these
measurements, we estimate a negative nonlinear refractive index for monolayer
graphene, $n_2 = - 1.1\times 10^{-13} m^2/W$. This is in contradiction to
previously reported values, which leads us to compare our experimental
measurements obtained by the OHD-OKE and the Z-scan method with theoretical and
experimental values found in the literature, and to discuss the discrepancies,
taking into account parameters such as doping.
