Real-world networks often possess underlying metric structures. Motivated by this observation, recent studies have embedded networks from diverse application domains into latent spaces, particularly from a hyperbolic geometry perspective. However, empirical comparisons between nodes’ real geographic locations and their corresponding latent representations remain limited. A clear understanding of the embedding outcomes is essential for both theoretical research and practical applications. In this work, we propose a novel Euclidean-space network embedding method and conduct a systematic comparison between nodes’ real geographic positions and their inferred latent locations in real networks. Our results provide deeper insights into the structure of the hidden space and its relationship with physical geography. Furthermore, we apply the learned latent representations to the link prediction task, which aims to identify potential connections using incomplete network information. Experimental results show that the proposed method achieves competitive link-prediction accuracy across multiple real-world networks, while providing an interpretable latent-space representation at relatively low computational cost. Overall, this work offers an interpretable and geographically informed solution for large-scale network embedding, with particular advantages for geography-sensitive network applications.
After the publication of the above article, we identified numerical artifacts in our work arising from the Euler–Maruyama integration scheme. We have carefully re-examined the theoretical formulation and repeated the numerical simulations. The corrected analysis partially modifies quantitative results reported in the original publication. However, the principal qualitative conclusions and the physical interpretation of the work remain unchanged. We report the corrections to the paper’s results here.
