Recent studies on neural network quantization have demonstrated a beneficial compromise between accuracy, computation rate, and architecture size. Implementing a 3D Vertical RRAM (VRRAM) array accompanied by device scaling may further improve such networks’ density and energy consumption. Individual device design, optimized interconnects, and careful material selection are key factors determining the overall computation performance. In this work, the impact of replacing conventional devices with microfabricated, graphene-based VRRAM is investigated for circuit and algorithmic levels. By exploiting a sub-nm thin 2D material, the VRRAM array demonstrates an improved read/write margins and read inaccuracy level for the weighted-sum procedure. Moreover, energy consumption is significantly reduced in array programming operations. Finally, an XNOR logic-inspired architecture designed to integrate 1-bit ternary precision synaptic weights into graphene-based VRRAM is introduced. Simulations on VRRAM with metal and graphene word-planes demonstrate 83.5 and 94.1% recognition accuracy, respectively, denoting the importance of material innovation in neuromorphic computing.