It is well known that by dispersing nanoparticles in a fluid, the thermal conductivity of the resulting nanofluid tends to increase with the concentration of nanoparticles. However, it is not clear what the mechanism behind this phenomenon is. Raman spectroscopy is a characterization technique connecting the molecular and macroscopic world, and therefore, it can unravel the puzzling effect exerted by the nanomaterial on the fluid. In this work, we report on a comparative study on the thermal conductivity, vibrational spectra and viscosity of graphene nanofluids based on three different amides: N, N-dimethylacetamide (DMAc); N, N-dimethylformamide (DMF); and N-methyl-2-pyrrolidinone (NMP). A set of concentrations of highly stable surfactant-free graphene nanofluids developed in-house was prepared and characterized. A correlation between the modification of the vibrational spectra of the fluids and an increase in their thermal conductivity in the presence of graphene was confirmed. Furthermore, an explanation of the non-modification of the thermal conductivity in graphene-NMP nanofluids is given based on its structure and a peculiar arrangement of the fluid.