Transparent conducting electrodes (TCEs) require high transparency and low sheet resistance for applications in photovoltaics, photodetectors, flat panel displays, touch screen devices and imagers. Indium tin oxide (ITO), or other transparent conductive oxides, have typically been used, and provide a baseline sheet resistance (RS) vs. transparency (T) relationship. However, ITO is relatively expensive (due to limited abundance of Indium), brittle, unstable, and inflexible; moreover, ITO transparency drops rapidly for wavelengths above 1000 nm. Motivated by a need for transparent conductors with comparable (or better) RS at a given T, as well as flexible structures, several alternative material systems have been investigated. Single-layer graphene (SLG) or few-layer graphene provide sufficiently high transparency (≈97% per layer) to be a potential replacement for ITO. However, large-area synthesis approaches, including chemical vapor deposition (CVD), typically yield films with relatively high sheet resistance due to small grain sizes and high-resistance grain boundaries (HGBs). In this paper, we report a hybrid structure employing a CVD SLG film and a network of silver nanowires (AgNWs): RS as low as 22 Ω/□ (stabilized to 13 Ω/□ after 4 months) have been observed at high transparency (88% at λ = 550 nm) in hybrid structures employing relatively low-cost commercial graphene with a starting RS of 770 Ω/□. This sheet resistance is superior to typical reported values for ITO, comparable to the best reported TCEs employing graphene and/or random nanowire networks, and the film properties exhibit impressive stability under mechanical pressure, mechanical bending and over time. The design is inspired by the theory of a co-percolating network where conduction bottlenecks of a 2D film (e.g., SLG, MoS2) are circumvented by a 1D network (e.g., AgNWs, CNTs) and vice versa. The development of these high-performance hybrid structures provides a route towards robust, scalable and low-cost approaches for realizing high-performance TCE.