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In recent years, mobile robots are becoming ambitious and deployed in large-scale scenarios. Serving as a high-level understanding of environments, a sparse skeleton graph is beneficial for more efficient global planning. Currently, existing solutions for skeleton graph generation suffer from several major limitations, including poor adaptiveness to different map representations, dependency on robot inspection trajectories and high computational overhead. In this paper, we propose an efficient and flexible algorithm generating a trajectory-independent 3D sparse topological skeleton graph capturing the spatial structure of the free space. In our method, an efficient ray sampling and validating mechanism are adopted to find distinctive free space regions, which contributes to skeleton graph vertices, with traversability between adjacent vertices as edges. A cycle formation scheme is also utilized to maintain skeleton graph compactness. Benchmark comparison with state-of-the-art works demonstrates that our approach generates sparse graphs in a substantially shorter time, giving high-quality global planning paths. Experiments conducted in real-world maps further validate the capability of our method in real-world scenarios. Our method will be made open source to benefit the community.