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Physics-based equivalent circuit models are presented for armchair and zigzag graphene nanoribbons (GNRs), and their conductances have been benchmarked against those of carbon nanotubes and copper wires. Atomically thick GNRs with smooth edges can potentially have smaller resistances compared with copper wires with unity aspect ratios for widths below 8 nm and stacks of noninteracting GNRs can have substantially smaller resistivities compared to Cu wires. It is shown that rough edges can increase the resistance of narrow GNRs by an order of magnitude. This fact highlights the need for patterning methods that can produce relatively smooth edges to fabricate low resistance GNR interconnects.