Temporal Hyperbolic Graph Representation Learning for Scale-Free Internet Routing and Delay Prediction

Predicting Internet round-trip time (RTT) is critical for routing optimization, quality-of-service (QoS) provisioning, and traffic engineering, yet remains challenging due to long-term temporal dependencies, evolving routing dynamics, and heavy-tailed latency distributions. While Temporal Graph Neural Networks (TGNNs) can model evolving network topologies, most existing approaches operate in Euclidean space, which poorly captures the hierarchical and scale-free structure of Internet routing graphs. Hyperbolic geometry provides a more suitable representation space. We propose HERMIT (Hyperbolic Edge-aware RTT Modeling via Integrated Topology), a hybrid framework combining a hyperbolic manifold-preserving temporal GNN with a Random Forest regressor for joint link prediction and RTT prediction. Built on HMPTGN, HERMIT introduces RTT-aware edge features and a learnable edge encoder to improve modeling of evolving link states and routing behavior. The resulting hyperbolic node representations are combined with historical RTT statistics for robust latency prediction. We evaluate HERMIT on a large-scale real Internet dataset spanning 2015-2024. HERMIT consistently outperforms a strong Random Forest baseline using only historical RTT statistics, achieving a 6% RMSE improvement while reducing large errors on heavy-tailed samples. It also surpasses prior hyperbolic TGNN models, including HMPTGN and HTGN, in link prediction performance. These results demonstrate that combining hyperbolic temporal graph learning with tree-based regression provides a scalable solution for RTT prediction in real-world Internet topologies.