We determined the frequency dependent effective permittivity of a large ternary network of randomly positioned resistors, capacitors, and diodes. A linear circuit analysis of such systems is shown to match the experimental dielectric response of single-walled carbon nanotube (SWCNT) filled polymers. This modeling method is able to reproduce the two most important features of SWCNT filled composites, i.e., the low frequency dispersion and dipolar relaxation. As a result of the modeling important physical conclusion proved by the experimental data was done: the low frequency behavior of SWCNT-filled polymer composites is mostly caused by the fraction of semiconducting SWCNTs.