Temporal Hyperbolic Graph Representation Learning for Scale-Free Internet Routing and Delay Prediction
Authors: Yi-Ling Kuo, Hao-Yu Tien, Shih-Yu Tsai
Organizations: Department of Information Management and Finance, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
Abstract
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.
Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare. We benchmark 13 unsupervised hyperbolic graph embedders under a unified protocol for link prediction and topology reconstruction on synthetic and empirical networks. The protocol captures both missing-link recovery and the preservation of local and global network structure. Maximum-likelihood and representation-learning-based approaches, including hybrid variants, achieve the strongest overall performance, although no method dominates across all tasks and structural regimes. Performance is more strongly associated with embedding paradigm than with disciplinary origin. We identify the network regimes in which different paradigms succeed or fail and provide practical guidance for method selection in downstream applications.
Robert Jankowski, Maksim Kitsak, Dorota Celińska-Kopczyńska
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result, numerous hyperbolic graph representation learning methods have been proposed in recent years. However, their practical adoption and systematic comparison remain challenging, as implementations are fragmented and shared tools for reproducible and fair evaluation are lacking. In this work, we introduce a unified open-source framework for hyperbolic graph representation learning that integrates several widely used embedding methods under a common optimization interface. The novel framework enables consistent training, visualization, and evaluation of hyperbolic embeddings, and interfaces seamlessly with standard network analysis tools. Leveraging this unified setup, we conduct an experimental study of hyperbolic embedding methods on real-world networks, focusing on two canonical downstream tasks: link prediction and node classification. Beyond predictive accuracy, the study offers practical insights into the strengths and limitations of existing approaches, thereby facilitating informed method selection and fostering reproducible research in hyperbolic graph representation learning.
As a core task in intelligent transportation systems, traffic forecasting plays a critical role in urban traffic management. Accurate traffic forecasting relies on modeling complex spatiotemporal dependencies, which is inherently challenging due to spatial heterogeneity in traffic systems.Despite significant progress, most existing methods are still limited to pairwise spatial dependency modeling, making it difficult to capture dynamic high-order interactions among nodes with similar traffic patterns. To address this issue, we propose PHGNet, a novel spatiotemporal forecasting framework based on prototype-guided hypergraph construction. At the core of PHGNet, a prototype learning mechanism is designed to adaptively assign pattern-similar nodes to hyperedges, thereby capturing high-order interactions with time-varying structures. To improve the reliability of dynamic hypergraph construction, we further develop a global-local node representation module to extract time-consistent features. For forecasting, iterative residual refinement and Temporal Query Attention are introduced to improve forecasting accuracy while supporting efficient parallel decoding. Extensive experiments on multiple real-world datasets demonstrate that PHGNet achieves superior predictive performance compared with state-of-the-art methods.