In the context of green communication and the carbon peaking &.carbon neutrality goals,enhancing network energy efficiency(EE)is one of the key technologies for the design and reliable operation of wireless communication systems.Firstly,this article presents the construction of a network consisting of paired fixed communication links to address the problem of maximizing energy efficiency in flexible duplex networks(Flex-Net).Subsequently,taking into account the benefits of graph neural networks in optimizing communication network resources,we propose a new architecture called GFlex-Net based on the graph neural network(GNN)framework.This architecture aims to jointly optimize communication direction and transmission power,thereby achieving maximum network energy efficiency. Simulation results demonstrate that,when compared to traditional algorithms,the proposed architecture achieves nearly optimal performance,reaching 95%of the performance of exhaustive methods,while maintaining a lower computational complexity of O(n²).Furthermore,the algorithm showcases the advantages of GNN in resource optimization,including reduced sample complexity,improved scalability,and enhanced.