arXiv:2610.31432v1 Announce Type: new Abstract: A conventional embodied agent in an indoor environment builds a map by accumulating noisy real-world measurements and results from heavy inference to guide navigation. While the detailed measurements may differ due to scene changes or sensor settings, the unique topological structure of navigable passages or the connectivity between rooms may provide training-free guidance that complements local observations. We propose a sparse topometric graph as an efficient structural representation for robust indoor navigation, alleviating the need for fine-grained matching, which is computationally expensive, memory-intensive, and prone to real-world variations. The map consists of nodes that encode local 3D geometry and distance-weighted edges that capture traversable connectivity. A learned graph-matching network finds consistent subgraph structures across sessions by considering both node-level geometric descriptors and neighborhood connectivity. The holistic contextual matching is robust to local ambiguities caused by weak distinctiveness or repetitive structure, and establishes stable correspondences despite local scene changes, different sensor modalities, or limited spatial overlap. We analyze the practicality of the graph through cross-session point-goal navigation, where a goal specified in a prior reference map must be reached from an unknown initial pose in a later session. Experiments show that our method achieves the highest success rates (77.1% on Gibson and 40.0% under 3D-FRONT scene changes), while reducing memory by more than two orders of magnitude compared to point-level representations. The proposed approach further supports cross-session alignment and goal-directed navigation with strong scalability and robust real-world transfer.