For achieving seamless global coverage and real-time communications while providing intelligent applications with increased quality of service (QoS), AI-enabled space–air–ground integrated networks (SAGINs) have attracted widespread attention from all walks of life. However, high-intensity interactions pose fundamental challenges for resource orchestration and security issues. Meanwhile, virtual network embedding (VNE) is applied to the function decoupling of various physical networks due to its flexibility. Inspired by the above, for SAGINs with non-Euclidean structures, we propose a graph-convolution virtual network embedding algorithm. Specifically, based on the excellent decision-making properties of deep reinforcement learning (DRL), we design an orchestration network combined with graph convolution to calculate the embedding probability of nodes. It fuses the information of the neighborhood structure, fully fits the original characteristics of the physical network, and utilizes the specified reward mechanism to guide positive learning. Moreover, by imposing security-level constraints on physical nodes, it restricts resource access. All-around and rigorous experiments are carried out in a simulation environment. Finally, results on long-term average revenue, VNR acceptance ratio, and long-term revenue–cost ratio show that the proposed algorithm outperforms advanced baselines.