Learning and Clustering on Temporal Graphs: Principles, Primitives, and Pooling
Authors: Nelson Aloysio Reis de Almeida Passos, Emanuele Carlini, Salvatore Trani
Organizations: University of Pisa, Dept. of Computer Science, 56127 Pisa PI, Italy · National Research Council, 56124 Pisa PI, Italy
Abstract
This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science. Although graph neural networks reach state-of-the-art performance across many downstream graph tasks, their advantage over established descriptive and inferential clustering algorithms is far less settled, especially under demands of efficiency and recovery accuracy. We frame this tension through three linked perspectives: principles, connecting graph learning and community detection through shared spectral foundations and detectability thresholds in stochastic block model regimes; primitives, making spectral clustering and multislice modularity optimization tractable through GPU-accelerated temporal backends; and pooling, viewing principled community detection as a theory-grounded coarse-graining operator for temporal graphs. Our results indicate that algorithmic methods remain the appropriate tool where attributes are absent or weak - scalability rather than accuracy being the binding obstacle - while neural models are most compelling when structural, temporal, and attribute signals align. By making temporal clustering scalable, GPU-accelerated primitives suggest a route toward theory-grounded pooling, while raising a central question: when does community-based coarse-graining preserve the dynamics needed for downstream learning tasks?
This work addresses community detection in temporal networks through GPU-accelerated extensions of spectral clustering and modularity-based algorithms originally designed for static graphs. Built on the NVIDIA RAPIDS ecosystem, the framework enables the characterization and tracking of communities in snapshot-based dynamic graphs, either by Leiden greedy optimization with multi-GPU support via Dask-based workload distribution, or eigendecomposition of a symmetric Bethe-Hessian operator. Our multislice modularity backend achieves up to roughly three orders of magnitude speedup over the CPU reference under an equal-work budget, depending on graph density and snapshot count, while preserving compatibility with existing graph analytics pipelines. We demonstrate its applicability on real-world and synthetic datasets, facilitating exploratory analysis of structural network properties over time. Such capabilities are relevant across several application domains, such as epidemic spreading, financial systems, cybersecurity, and trajectory and mobility analysis. We release our implementation as free and open-source software, including Python bindings through the NetworkX-Temporal library for ease of use and zero-code acceleration with existing codebases.
Nelson Aloysio Reis de Almeida Passos, Emanuele Carlini, Salvatore Trani
Temporal graph learning is commonly organized around the evolution of node states or the encoding of interaction histories. We study an underexplored, operator-centric question: should the graph propagation mechanism itself evolve over time? We introduce Dynamic Spectral Filtering (DSF), which represents propagation at snapshot t by a Chebyshev polynomial filter with vector-valued, time-dependent coefficients. DSF explicitly treats these compact multi-order coefficients as recurrent temporal states. A recurrent branch proposes updates, while multiplicative global and order-specific gates regulate their magnitude. The temporal state is independent of the number of nodes. On MOOC, Wikipedia, and Reddit temporal link-prediction benchmarks, converged DSF runs attain AP scores of 0.7851, 0.9088, and 0.9860, respectively, with 93K to 133K trainable parameters, 68 to 182 MB peak GPU memory, and 1.6 to 2.1 seconds of training per epoch. Against the closely related DEFT baseline, DSF is better on MOOC, within 0.001 AP on Reddit, and modestly lower on Wikipedia, while using 8.3 to 8.6 times fewer parameters, 25 to 33 times less GPU memory, and 5 to 19 times less time per epoch. Relative to all measured alternatives, it uses 3.3 to 38.6 times less GPU memory. These results support direct spectral-response evolution as a useful temporal inductive bias when computational efficiency is a first-class requirement.
Temporal graph learning has become essential for analyzing real-world systems whose interactions continuously evolve over time, including financial transaction networks, communication systems, and online social platforms. However, learning from large-scale temporal graphs remains computationally challenging when networks are dense and rapidly changing. To address this limitation, we propose a network-curvature-inspired edge sparsification framework for dynamic graph learning. Our proposed method, TRicci, extends classical Forman-Ricci curvature to directed weighted temporal graphs by capturing structural support, temporal recency, and local interaction competition. Experiments on 9 transaction networks and 3 temporal graph benchmark datasets demonstrate that the proposed framework preserves predictive performance across multiple graph-level prediction tasks. The results show that TRicci sparsifies temporal graphs by approximately 80% while reducing end-to-end downstream training and inference time by an average of 55.94%, without substantial degradation in predictive performance. Our findings suggest that temporal curvature can serve as a principled basis for scalable temporal graph learning by preserving predictive temporal-structural information under substantial sparsification.