Abstract: To address the common issues of high curtailment rates and line loss rates in the practical design of photovoltaic-storage microgrid topologies, a graph neural network-based optimization method for photovoltaic-storage microgrid topology design is proposed. By constructing an optimization model centered on minimizing the levelized cost of electricity while comprehensively considering equipment capacity and operational constraints, the intelligent and efficient optimization of microgrid topologies is achieved through the message-passing mechanism of graph neural networks. Experimental results demonstrate that the proposed method yields significant improvements, reducing the system curtailment rate to 2.8% and strictly controlling the line loss rate at 3.1%. Compared to traditional optimization methods, the approach achieves notable enhancements of 65.9% and 40.4%, respectively, effectively improving the system's economic operation level and renewable energy accommodation capacity, providing a novel solution for microgrid topology optimization.