The electronic conduction properties of copper–graphene composite materials including common coal impurities are studied. Exploring the transport properties for three crystallographic orientations [(111), (110), and (100)] of copper in copper–graphene composites, a strong orientational dependence on electronic conductivity is shown. Graphene exhibits near-ideal registries for (111) and (110) orientations, forming a connected network between grains that enables efficient carrier transport. The influence of non-carbon elements: nitrogen (N), oxygen (O), and sulfur (S) in graphene, representing possible structures in coal-based graphene are investigated. N, O, and S in graphene negatively impact the composite’s electronic conductivity relative to pristine graphene. A new method is introduced for visualizing the spatial distribution of electrical conduction activity in materials using the square of the electronic charge density near the Fermi level, based on the work of Mott. We call this technique the N2 method.