Temporal Link Prediction

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. \emph{Temporal-first} approaches build per-node temporal embeddings and only afterward perform spatial aggregation, whereas \emph{Spatial-first} approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; effectively, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's \emph{past} trajectory. This paper introduces \textbf{SiST-GNN} (\textbf{Si}multaneous \textbf{S}patial-\textbf{T}emporal \textbf{GNN}), which fuses the two signals inside a single message-passing operation rather than chaining them. At each snapshot, we maintain a recurrent hidden state per node that summarises its history, pairs it with the node's current feature vector, and treats the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. We compare against fourteen link-prediction baselines under both the fixed-split and live-update evaluation regimes, and eleven baselines on node classification. Across the public benchmarks, SiST-GNN improves on the strongest prior method in link prediction by 1-18% in the fixed-split setting, and is the leading learned method on five of six datasets in the live-update setting, improving on the strongest prior method by 1-158% there. We additionally derive three dynamic node-classification tasks by discretizing the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7-23% and matches continuous-time (CTDG) methods that consume the raw events directly.

Dynamic link prediction is important for modeling evolving interactions in complex systems, including social, communication, financial, and transportation networks. Classical temporal graph models capture sequential dependencies, but they may struggle to represent concurrent and rapidly changing node-edge interactions in large dynamic graphs. We propose A2QTGN (Adaptive Amplitude Quantum-Integrated Temporal Graph Network), a hybrid quantum-classical framework that combines adaptive amplitude encoding with a Temporal Graph Network backbone. The proposed mechanism represents node interaction features as quantum states and selectively refreshes amplitude embeddings based on temporal activity, preserving stable node states while emphasizing meaningful structural changes. This design reduces unnecessary quantum re-encoding and improves temporal representation for link prediction. Experiments on five Temporal Graph Benchmark datasets show that A2QTGN achieves strong predictive and ranking performance across diverse dynamic graphs. Ablation studies confirm the importance of both the quantum embedding module and the adaptive update strategy, while hardware-aware inference using a noisy backend and limited real-device execution supports the feasibility of near-term quantum-assisted temporal graph learning.

Temporal Knowledge Graph Reasoning (TKGR) aims at inferring missing (especially future) events from historical data. Current evaluation in TKGR uniformly weights all events, ignoring that most are trivial repetitions, which overestimate the true reasoning ability. Therefore, the rare outstanding events, whose prediction demands deeper reasoning, should be distinguished and emphasized. To this end, we propose a strikingness-aware evaluation framework, which introduces a rule-based strikingness measuring framework (RSMF) to quantify event strikingness by comparing its expected occurrence with peer events derived from temporal rules. Strikingness is then integrated as a weighting factor into metrics like weighted MRR and Hits@k. Experiments on four TKG benchmarks reveal: 1) All representative models perform worse as event strikingness increases, 2) Path-based methods excel on low-strikingness events and representation-based ones on high-strikingness events, 3) We design an ensemble method whose gains stem from fitting trivial events rather than reasoning improvement. Our framework provides a more rigorous evaluation, refocusing the field on predicting outstanding events.

Dynamic text-attributed graphs (DyTAGs) provide a powerful framework for modeling evolving systems in which node semantics and time-dependent interactions are tightly coupled. Recently, multimodal learning has emerged as a promising yet underexplored direction for enhancing DyTAG representation learning. However, existing methods typically rely on rigid modality partitions and one-shot fusion strategies, which limit their ability to capture the intrinsic and evolving dependencies between node semantics and interaction behaviors. To address these limitations, we propose \textbf{PRISM}, an iterative cross-modal posterior refinement framework for DyTAG representation learning. PRISM organizes DyTAG information into semantic and behavioral modalities, providing a more intrinsic alternative to carrier-level modality partitions. Instead of fusing the two modalities in a single step, PRISM learns a refinement trajectory that progressively transforms semantic priors into behavior-conditioned posterior states through cross-modal interaction with behavioral evidence. Extensive experiments on DTGB benchmark datasets show that PRISM achieves strong performance on temporal link prediction and destination node retrieval tasks. Further ablation studies validate the effectiveness of semantic--behavioral modeling and iterative posterior refinement.

Temporal knowledge graph (TKG) reasoning aims to predict future events from historical facts. A key challenge lies in jointly capturing two sources of predictive information in TKGs: historical evidence and evolutionary dynamics. However, existing methods typically focus on only one of these sources, which limits the ability to fully exploit the complementary predictive signals in TKGs. To address this, we propose CHE-TKG, a novel collaborative dual-view learning framework for TKG reasoning. CHE-TKG explicitly separates and jointly models historical evidence and evolutionary dynamics, aiming to learn and exploit their complementary predictive signals. Specifically, CHE-TKG constructs a historical evidence graph to capture long-term structural regularities and stable relational constraints, alongside an evolutionary dynamics graph to model temporal transitions and recent changes, with dedicated encoders for each view. We further employ relation decomposition and a contrastive alignment objective to better capture the predictive signals across the two views. Extensive experiments demonstrate that CHE-TKG achieves state-of-the-art performance on multiple benchmarks.

Accurate prediction of physician referral links is essential for optimizing care coordination and reducing fragmentation in healthcare delivery. However, existing computational methods, ranging from triadic closure heuristics to graph neural networks, fail to capture the intrinsic properties of physician referral networks, including sparsity, disassortative degree mixing, and hub-dominated topology. Here, we propose H3, a healthcare three-hop index that addresses these limitations by modeling indirect referral pathways through intermediate physicians, with degree-based normalization and a redundancy penalty to mitigate hub-mediated noise. Using Medicare Physician Shared Patient Patterns data, we evaluate H3 under two complementary prediction regimes: within-period prediction, which assesses recovery of contemporaneous referral links under sparse conditions, and cross-period prediction, which tests robustness to temporal shift as referral windows expand. Across both regimes, H3 consistently outperforms classical heuristics and deep learning-based baselines. Unlike black-box neural network approaches, H3 produces fully decomposable predictions traceable to specific intermediary physicians, offering a transparent and deployable solution for referral network completion.

Temporal knowledge graph (TKG) extrapolation is an important task that aims to predict future facts through historical interaction information within KG snapshots. A key challenge for most existing TKG extrapolation models is handling entities with sparse historical interaction. The ontological knowledge is beneficial for alleviating this sparsity issue by enabling these entities to inherit behavioral patterns from other entities with the same concept, which is ignored by previous studies. In this paper, we propose a novel encoder-decoder framework OntoTKGE that leverages the ontological knowledge from the ontology-view KG (i.e., a KG modeling hierarchical relations among abstract concepts as well as the connections between concepts and entities) to guide the TKG extrapolation model's learning process through the effective integration of the ontological and temporal knowledge, thereby enhancing entity embeddings. OntoTKGE is flexible enough to adapt to many TKG extrapolation models. Extensive experiments on five data sets demonstrate that OntoTKGE not only significantly improves the performance of many TKG extrapolation models but also surpasses many state-of-the-art(SOTA) baseline methods.

Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs and thus struggle to capture temporal dependencies. Snapshot-based techniques partially address this issue but often encounter data sparsity and class imbalance, particularly in networks with transient interactions such as telecommunication call detail records (CDRs). Temporal Graph Networks (TGNs) model dynamic graphs by updating node embeddings over time; however, their predictive accuracy under sparse conditions remains limited. In this study, we improve the TGN framework by extracting enclosing subgraphs around candidate links, enabling the model to jointly learn structural and temporal information. Experiments on a sparse CDR, email, message dataset show that our approach increases average precision by at least 2% over standard TGNs, demonstrating the advantages of integrating local topology for robust link prediction in dynamic networks.

Learning on temporal graphs has become a central topic in graph representation learning, with numerous benchmarks indicating the strong performance of state-of-the-art models. However, recent work has raised concerns about the reliability of benchmark results, noting issues with commonly used evaluation protocols and the surprising competitiveness of simple heuristics. This contrast raises the question of which characteristics of the underlying graphs temporal graph learning models actually use to form their predictions. We address this by systematically evaluating eight models on their ability to capture eight fundamental characteristics related to the link structure of temporal graphs. These include structural characteristics such as density, temporal patterns such as recency, and edge formation mechanisms such as homophily. Using both synthetic and real-world datasets, we analyze how well models learn these characteristics. Our findings reveal a mixed picture: models capture some characteristics well but fail to reproduce others. With this, we expose important limitations. Overall, we believe that our results provide practical insights for the application of temporal graph learning models and motivate more interpretability-driven evaluations in graph learning research.

Temporal graph learning is crucial for dynamic networks where nodes and edges evolve over time and new nodes continuously join the system. Inductive representation learning in such settings faces two major challenges: effectively representing unseen nodes and mitigating noisy or redundant graph information. We propose GTGIB, a versatile framework that integrates Graph Structure Learning (GSL) with Temporal Graph Information Bottleneck (TGIB). We design a novel two-step GSL-based structural enhancer to enrich and optimize node neighborhoods and demonstrate its effectiveness and efficiency through theoretical proofs and experiments. The TGIB refines the optimized graph by extending the information bottleneck principle to temporal graphs, regularizing both edges and features based on our derived tractable TGIB objective function via variational approximation, enabling stable and efficient optimization. GTGIB-based models are evaluated to predict links on four real-world datasets; they outperform existing methods in all datasets under the inductive setting, with significant and consistent improvement in the transductive setting.

Functional Magnetic Resonance Imaging (fMRI) is an imaging technique widely used to study human brain activity. fMRI signals in areas across the brain transiently synchronise and desynchronise their activity in a highly structured manner, even when an individual is at rest. These functional connectivity dynamics may be related to behaviour and neuropsychiatric disease. To model these dynamics, temporal brain connectivity representations are essential, as they reflect evolving interactions between brain regions and provide insight into transient neural states and network reconfigurations. However, conventional graph neural networks (GNNs) often struggle to capture long-range temporal dependencies in dynamic fMRI data. To address this challenge, we propose BrainATCL, an unsupervised, nonparametric framework for adaptive temporal brain connectivity learning, enabling functional link prediction and age estimation. Our method dynamically adjusts the lookback window for each snapshot based on the rate of newly added edges. Graph sequences are subsequently encoded using a GINE-Mamba2 backbone to learn spatial-temporal representations of dynamic functional connectivity in resting-state fMRI data of 1,000 participants from the Human Connectome Project. To further improve spatial modeling, we incorporate brain structure and function-informed edge attributes, i.e., the left/right hemispheric identity and subnetwork membership of brain regions, enabling the model to capture biologically meaningful topological patterns. We evaluate our BrainATCL on two tasks: functional link prediction and age estimation. The experimental results demonstrate superior performance and strong generalization, including in cross-session prediction scenarios.

Temporal graph networks suffer from irregular supervision in realworld dynamic graphs, as most minibatches contain few labeled events. The lack of labels leads to high-variance gradient updates and, consequently, slow wall-clock convergence. To constructively reduce sparsity, our Moving-Averaged Labels (MAL) assigns soft pseudo-targets based on past supervised signals using a running label distribution while leaving the loss and the model architecture unchanged. Thus, supervision gaps are replaced with informative signals independent of a temporal graph model and the message passing or memory components used. Theoretical analysis supports our insight that aggregating historical supervision into moving average targets reduces stochastic gradient variance, yielding faster convergence under mild assumptions. Experimentally, for TGNv2 and DyRepv2 (our modification of DyRep) models, MAL boosts predictive performance, establishing a new SOTA, and improves time-to-accuracy (on average 6x faster to reach the top score) for a common suite of Temporal Graph Benchmark datasets.

Aggregating temporal signals from historic interactions is a key step in future link prediction on dynamic graphs. However, incorporating long histories is resource-intensive. Hence, temporal graph neural networks (TGNNs) often rely on historical neighbors sampling heuristics such as uniform sampling or recent neighbors selection. These heuristics are static and fail to adapt to the underlying graph structure. We introduce FLASH, a learnable and graph-adaptive neighborhood selection mechanism that generalizes existing heuristics. FLASH integrates seamlessly into TGNNs and is trained end-to-end using a self-supervised ranking loss. We provide theoretical evidence that commonly used heuristics hinder TGNNs performance, motivating our design. Extensive experiments across multiple benchmarks demonstrate consistent and significant performance improvements for TGNNs equipped with FLASH.