The hierarchical structure of semidilute suspensions of single-walled carbon nanotubes in polymeric matrices, studied by the use of ultrasmall and small angle neutron scattering, indicates an aggregate size that is independent on both nanotube concentration and polymer matrix and a mesh within the floc that becomes slightly denser with increasing nanotube concentration. The number of clusters grows linearly with concentration of nanotubes. These structural parameters suggest that the interactions between the flocs dictate the concentration-dependent elastic strength scaling of the network, with the absolute values of the specific elastic strength being inversely related to the percolation threshold.