This work aims to construct a management system capable of automatically detecting, analyzing, and responding to network security threats, thereby enhancing the security and stability of networks. It is based on the role of artificial intelligence (AI) in computer network security management to establish a network security system that combines AI with traditional technologies. Furthermore, by incorporating the attention mechanism into Graph Neural Network (GNN) and utilizing botnet detection, a more robust and comprehensive network security system is developed to improve detection and response capabilities for network attacks. Finally, experiments are conducted using the Canadian Institute for Cybersecurity Intrusion Detection Systems 2017 dataset. The results indicate that the GNN combined with an attention mechanism performs well in botnet detection, with decreasing false positive and false negative rates at 0.01 and 0.03, respectively. The model achieves a monitoring accuracy of 98\%, providing a promising approach for network security management. The findings underscore the potential role of AI in network security management, especially the positive impact of combining GNN and attention mechanisms on enhancing network security performance.