Herein, stacks of graphene nanosheets resulting from an incomplete dispersion of nanoparticles in polymer graphene nanocomposites are considered. The volume fraction, aspect ratio and conduction of stacks are expressed by the distance between nanosheets (s), thickness of an individual nanosheet (t), nanosheet diameter (D), thickness of the interphase zone (ti) and tunneling length (d). Moreover, the percolation onset, actual filler quantity and portion of networked nanosheets are stated by the stacks of nanosheets, interphase depth and tunneling length. Finally, an advanced model for the conductivity of a graphene-based system is presented using the mentioned terms. The influence of all properties of stacks, tunneling and interphase areas on the percolation onset, portion of percolated nanosheets and conductivity are examined. Furthermore, the tested values of conductivity are applied to confirm the predictability of the model. The larger quantity of thin sheets included in stacks produces a higher conductivity for samples. In addition, a thicker interphase and smaller tunnels can result in higher conductivity. The calculations of conductivity match the tested data at all filler amounts.