We investigate the static properties of monodisperse polymer/single wall carbon nanotube (SWCNT) nanocomposites in comparison to polymer melts by molecular dynamics simulations. The SWCNT has a large aspect ratio and radius smaller than the polymer radius of gyration. We find that although the local chain structure is significantly affected, the overall configuration, as characterized by the radius of gyration, is not perturbed either by the interaction strength between the polymer and the SWCNT or by variations in the SWCNT radius.