This article addresses the challenges of registering two rigid semantic scene graphs, an essential capability when an autonomous agent needs to register its map against a remote agent, or against a prior map. The handcrafted descriptors in classical semantic-aided registration, or the ground-truth annotation reliance in learning-based scene graph registration, impede their application in practical real-world environments. To address the challenges, we design a scene graph network to encode multiple modalities of semantic nodes: open-set semantic feature, local topology with spatial awareness, and shape feature. These modalities are fused to create compact semantic node features. The matching layers then search for correspondences in a coarse-to-fine manner. In the back end, we employ a robust pose estimator to decide transformation according to the correspondences. We manage to maintain a sparse and hierarchical scene representation. Our approach demands fewer GPU resources and fewer communication bandwidth in multiagent tasks. Moreover, we design a new data generation approach using vision foundation models and a semantic mapping module to reconstruct semantic scene graphs. It differs significantly from previous works, which rely on ground-truth semantic annotations to generate data. We validate our method in a two-agent simultaneous localization and mapping benchmark. It significantly outperforms the handcrafted baseline in terms of registration success rate. Compared to visual loop closure networks, our method achieves a slightly higher registration recall while requiring only 52 kB of communication bandwidth for each query frame.