In earlier experiments  we found there was significant transmission of THz radiation through carbon-fiber enforced composites, despite that fact that the dc conductivity of the carbon fibers is expected to be good and hence should prevent penetration of electro-magnetic radiation. To study the relationship between absorption of THz radiation and electrical conductivity we performed measurements on samples with different concentrations of graphene in an epoxy matrix. We observed an increased absorption of THz radiation with increased graphene concentration. Our conductivity measurements (simple transverse DC measurements using tin foil as electrodes that cover the two sample surfaces) showed the typical increase of several orders of magnitude with graphene concentration. Although both the conductivity and the THz absorption increase with graphene concentration, there is no direct cause-and-effect relation between the two quantities. Careful analysis shows that even the highest dc conductivity values cannot explain even the lowest observed values for the THz absorption coefficient.