Nanorod dispersions possess remarkable macroscopic property enhancements due to percolation in the rod phase. Yet, quantitative and predictive property assessment tools do not exist except at the isotropic percolation threshold. We lay the foundation for these tools. We build a tight connection between 1) complex networks, their graph representations, and graph analysis, and 2) electrical properties of composites consisting of conducting rods or fibers dispersed in a poorly conducting matrix. We are interested in sheared thin films of nanorod dispersions which are typically well above percolation threshold to insure a high probability of percolation. Properties are likewise anisotropic due to the shear-induced anisotropy of the nanorod orientational distribution and of percolating paths within the rod phase for which existing theories and property assessment tools are inadequate. We develop multi-resolution electrical property metrics based on percolation in the particle phase and reflective of the statistical mechanics and anisotropy of sheared Brownian dispersions. These tools and theories can provide valuable guidance for manufacturing new functional materials.