Nano-topology is a unique topology induced by rough approximation spaces, which consist of approximation operators and boundary regions. This study presents an innovative topology derived from graphs and applies it to generate a novel rough set model. We investigate the primary characteristics of this model and compare it with previous ones. The paper concludes with an application demonstrating the use of graph nano-homeomorphism to establish the equivalence of electrical circuits. The results indicate that the proposed approach enhances classification measurement performance compared to earlier methods, effectively modeling the inherent complexity of electrical circuits. This improvement suggests that our method provides a more robust framework for developing mechanisms in electrical circuits, which is vital for advancing electrical research.