By mimicking the brain's efficient spiking encoding paradigm, spiking graph neural networks exhibit significant potential for efficient graph data analysis. Due to the inherent expressive limitations of binary spiking signals adopted in spiking encoding, existing models typically enhance their expression by integrating numerous real-valued multiplication-additions or high-latency encoding. However, such integrations compromise the core efficiency superiority of spiking models, limiting their scalability in real-world applications. To simultaneously reconcile considerable expression and efficiency, we propose E2SGNN, a novel network comprising a dual-scale modulated spiking backbone and a latency-dynamic optimization module. The former backbone integrates global and local real-valued graph modulations into spiking graph convolution, enabling discriminative dual-scale neighbor embedding in the encoding process. It both breaks through binary spiking signals' expressive limitations and improves the content expressiveness of spiking graph representations, while retaining low-latency and addition-only efficient advantages. Moreover, to further reduce the latency redundancy for higher efficiency, the latter module adaptively customizes the latency for each graph data based on data complexity. In this way, our network can finally generate graph representations expressively and efficiently. Experiments on various datasets demonstrate the superiority of our network in expression and efficiency.
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A significant challenge in developing graph foundational models is to achieve universality and generalizability across general graphs, beyond text-attribute graphs. Unfortunately, most graph neural networks are designed for specific applications in particular fields and are difficult to generalize across different graphs. The most critical problem is the lack of Transfer Invariant Metadata (TIM) for graphs, akin to pixels for images and vocabularies for text, which prevents the development of graph foundational models. TIM is particularly problematic, albeit critical, on graph nodes with semantically variable features, making it difficult to transfer knowledge across graphs. Here, we analyze TIM and propose a theoretical approach to mining TIM in node features. It extracts semantically consistent information across domains and unifies data space with relatively low information loss. We then introduce a Transfer-Invariant Graph (TIG) foundational model to transform features of different dimensions into a unified structural representation. This transformation can effectively learn and extract TIM and intrinsic graph knowledge by self-supervised learning. We conducted extensive experiments, and the results showed that TIG even outperformed some models trained on data from targeted domains. In one-shot cross-domain scenarios, TIG achieved high accuracy with less training data and without any prompt tuning.
Text-Attributed Graph (TAG) is an important type of graph structured data, where each node has a text description. TAG models usually train a Graph Neural Network (GNN) and language model jointly, which leads to high space and time consumption, especially on large datasets. To mitigate this, we propose TAGSAM, a condensation method that compresses TAGs while preserving training accuracy. TAGSAM comes with two key designs, i.e., subgraph text Selection and Attribute similarity Matching, which compress the text description and graph topology of TAG, respectively. For the texts, subgraph text selection selects and merges representative text chunks from multiple related text descriptions by maximizing mutual information. For the graph topology, popular condensation methods based on Matching Training Trajectories (MTT) suffer from high variance, which hinders accuracy. Our attribute similarity matching mitigates this issue by aligning stable similarity matrices. We evaluate TAGSAM against six state-of-the-art baselines, where it showcases superior performance. For the same compressed size, TAGSAM improves upon the best-performing baseline by an average of 4.9% in accuracy. Furthermore, it maintains competitive training accuracy even when the TAG is condensed to just 1% size. Our code is available at https://github.com/SundayVHan/TAGSAM
Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that naturally arise when training and test data follow similar but non-identical distributions. As the generation of dynamic graphs is strongly influenced by latent environments, it is critical to investigate their impacts on the generalization behavior of DyGNNs. We therefore establish a connection between the temporal message-passing scheme employed by DyGNNs and their generalization performance under distribution shifts. Our analysis reveals that environment-specific factors misguide the learning process and lead to unsatisfactory out-of-distribution (OOD) generalization. Based on this insight, we propose MoVE, a Mixture of Variational Experts network to mitigate complex distribution shifts in dynamic graphs. MoVE adopts a hierarchical variational architecture that extrapolates latent representations into a mixture of distribution shifts as pseudo-environments. Additionally, we incorporate a Mixture-of-Experts (MoE) framework with a novel training objective that aligns the outputs of different experts to produce invariant representations. Extensive experiments on various dynamic graphs, including both real-world and synthetic datasets, demonstrate that our model significantly outperforms state-of-the-art techniques.
Model transferability estimation is a task-adaptive pre-trained model selection problem, aiming to determine the optimal model for target dataset from a model hub pre-trained on source dataset without fine-tuning. Although existing model transferability evaluation methods have made some progress, they mainly focus on image or text data in CV and NLP. In contrast, the graph structural data with GNNs models is still underexplored, due to the complexity of the graph structure and the limitations of the generalization ability of GNN models under distribution shift. To fill this blank, we first propose a Graph Neural Network Model Transferability Estimation method via decomposition-augmented discriminant analysis, named GNNMTE, to evaluate the transferability of GNN models on target graph dataset without fine-tuning. It only calculates the GNNMTE score to determine whether it can be effectively transferred to target graph dataset and better select the optimal model for the target graph dataset. Specifically, our proposed \method contains three core components: (1) Dual-block SVD fusion for obtaining the corresponding principal component information; (2) Adaptive weighting by singular value ratio for guiding the extraction of important principal component information on graph data; (3) Graph discriminant analysis for finding the optimal projection direction that separates the classes of graph data. Extensive experimental results on cross-domain graph datasets achieve excellent results, demonstrating powerful superiority.
Graph-structured data effectively captures complex relationships in diverse domains such as social networks, financial transactions, citation networks, and recommendation systems. Graph Neural Networks (GNNs) excel in learning intricate topological patterns, yielding strong performance on tasks like node classification and link prediction. However, real-world graphs often scale to millions of nodes and billions of directed edges, posing significant computational and storage challenges for GNN training that frequently exceed available hardware limits. Although graph sampling and distillation techniques alleviate these issues by subsampling or creating surrogate graphs, they primarily handle undirected graphs, neglecting directional semantics that are crucial for applications like fraud detection and causal analysis. To address these limitations, we introduce the Directed Graph Distillation (Dir-GD) framework, which combines distributed learning with community detection to divide large directed graphs into independent subgraphs for distributed directed GNN training. This process culminates in parameter aggregation to produce a compact global synthetic graph that preserves essential topology and directionality. Extensive experiments on large-scale datasets, such as the million-node soc-pokec-relationships, demonstrate over 91% accuracy at 0.001 distillation ratios, accompanied by substantial memory and runtime savings. This work pioneers directed graph distillation as a key paradigm for analyzing ultra-large directed graphs, offering a scalable solution that maintains high fidelity in compressed representations.
Signed Graph Neural Networks (SGNNs) have achieved outstanding performance in Link Sign Prediction (LSP), which involves predicting the existence and polarity of edges, by effectively modeling positive and negative interactions in signed graphs. However, their black-box nature raises transparency concerns, necessitating faithful explanations of model behavior to ensure trustworthiness and accountability. Existing eXplainable GNN (XGNN) methods, primarily designed for unsigned graphs, struggle to provide meaningful and human-understandable explanations for SGNN-based LSP, often generating disconnected subgraph explanations or neglecting the unique sign interactions. To address the gap, we propose SGExplainer, a novel method that leverages balanced paths, a concept rooted in signed graph theory, to provide clear and faithful explanations for LSP. SGExplainer employs a path-enforcing mask learning framework that ensures interpretable balanced path generation while maintaining explanation fidelity. Extensive experiments on real-world signed graphs demonstrate that SGExplainer consistently provides faithful and intuitive explanations for various SGNNs, outperforming state-of-the-art baselines in explanation quality, interpretability, and efficiency.
Graph-based fraud detection (GFD) aims to identify fraud nodes within graph-structured data that significantly deviate from the majority of benign nodes. However, existing graph neural networks (GNNs) often struggle in GFD scenarios due to their reliance on homophily assumption, which is frequently violated by the inherent homophily-heterophily mixture of fraud graphs. Moreover, most methods focus primarily on local topology, overlooking mesoscopic community structures, making them less efficient in detecting suspicious patterns like densely connected subgraphs. To address the aforementioned issues, we present NeCo, a novel approach that integrates mixture of neighborhood and community experts for graph-based fraud detection. Specifically, we first introduce a fraud-discriminative representation preservation mechanism from a neighborhood perspective, leveraging the empirical finding that fraud nodes tend to exhibit larger feature propagation discrepancies compared to benign nodes. We then design a community-oriented node representation module that models structural compactness among nodes, enabling the detection of suspicious topological patterns associated with fraud behaviors. By integrating these two complementary perspectives, NeCo can effectively captures both local inconsistency and global structural irregularity. Extensive experiments across five real-world datasets demonstrate the effectiveness of our proposed NeCo over state-of-the-art baselines.
Real-world temporal graphs are largely driven by sequential dynamics, and edge repetitions are rare. This characteristic has spotlighted a key limitation of existing temporal graph neural networks (T-GNNs): on such graphs, state-of-the-art T-GNNs often achieve less than 70% MRR on link prediction. Two factors drive this shortfall: (1) Memory modules and neighbor co-occurrence encodings in existing T-GNNs often fail since they rely on memorizing exact neighbor identities and on the co-occurrence assumption. (2) Existing T-GNNs are sensitive to abrupt events, which are common in sequential settings that can exceed ten million updates, thereby compromising generalization. To tackle the challenges of sequential dynamics, we propose SeqFilter, a simple yet robust neural network that functions as a composite filter for link prediction on temporal graphs. SeqFilter comprises two modules: a node rhythm memory and a frequency-selective structure encoder. The node rhythm memory shifts the focus from who interacts to when, modeling absolute timestamps with recency awareness to capture each node's interaction rhythm. To model temporal structures in complex sequential dynamics, we propose a frequency-selective structure encoder that amplifies or suppresses specific frequencies in the neighbor spectrum, enabling the effective modeling of local structure correlations. Theoretically, this encoder functions as a cascade of three learnable filters that approximate the optimal linear denoiser, helping capture the underlying structural patterns. Last, SeqFilter fuses the outputs of two modules to generate high-quality node embeddings. Extensive experiments across eight sequential dynamic datasets show that SeqFilter outperforms 11 baselines by an average improvement of 15.82% in MRR while achieving an order of magnitude speedup compared to the frequency-enhanced baseline.
Recently, Graph Foundation Models (GFMs) have emerged as a central focus in the field of graph learning due to their strong generalizability to various unseen graphs. However, existing GFMs typically work under the homophily assumption, and the exploration of universality on heterophilic graphs is still in its early stages. In fact, even in homophilic graphs, there exists limited yet informative heterophilic information that is not fully exploited by current GFMs. Moreover, due to the requirement for universality, the heterophily issue faced by GFMs is more challenging than in classical graph learning, as it requires training a single model to adapt to varying structures, features, and tasks. Classic heterophilic graph learning methods primarily based on the node-level homophily or heterophily. However, we highlight that homophily and heterophily exist not only at the node semantic level, but also at a finer granularity across individual feature dimensions. This finding enables GFMs to adapt to heterophilic graphs and better utilize the small amount of heterophilic information in homophilic graphs. Based on this, we propose Topology-aware Feature Sorting Graph Foundation Model (TFSGFM), which employs a feature-level topology-aware sorting strategy and a dual-channel graph neural network framework, enabling unified modeling of both feature and structure. Extensive experiments demonstrate the strong generalizability of TFSGFM. The source code is available at https://github.com/hedongxiao-tju/TFSGFM.
Liquid Time-Constant networks (LTCs), a type of continuous-time graph neural network, excel at modeling irregularly-sampled dynamics but are fundamentally confined to Euclidean space. This limitation introduces significant geometric distortion when representing real-world graphs with inherent non-Euclidean structures (e.g., hierarchies and cycles), degrading representation quality. To overcome this limitation, we introduce the Riemannian Liquid Spatio-Temporal Graph Network (RLSTG), a framework that unifies continuous-time liquid dynamics with the geometric inductive biases of Riemannian manifolds. RLSTG models graph evolution through an Ordinary Differential Equation (ODE) formulated directly on a curved manifold, enabling it to faithfully capture the intrinsic geometry of both structurally static and dynamic spatio-temporal graphs. Moreover, we provide rigorous theoretical guarantees for RLSTG, extending stability theorems of LTCs to the Riemannian domain and quantifying its expressive power via state trajectory analysis. Extensive experiments on real-world benchmarks demonstrate that, by combining advanced temporal dynamics with a Riemannian spatial representation, RLSTG achieves superior performance on graphs with complex structures. Project Page: https://rlstg.github.io
Unsupervised graph domain adaptation (UGDA) aims to transfer knowledge from a labeled source graph to an unlabeled target graph, addressing the performance degradation caused by distributional shifts in node attributes and graph structures across domains. Despite recent progress, existing UGDA approaches still face two key challenges: (C1) Data-level: Most methods rely on a single source domain, overlooking the complementary knowledge that could be leveraged from multiple sources. (C2) Model-level: Many UGDA models emphasize complex, handcrafted Graph neural network (GNN) architectures, while simpler yet effective designs with propagation (P) & transformation (T) pipeline remain underexplored. To address these challenges, in this paper, we propose a novel approach, which leverages Concise Propagation–Transformation pipeline for multi-source unsupervised Graph Domain Adaptation, dubbed as CPT-GDA, to better capture complementary knowledge from multiple sources in an efficient manner. Specifically, the proposed CPT-GDA adopts a dual-branch GNN architecture with different depths of propagation but the same P-T patterns, which enables the model to efficiently learn node representations to mitigate domain discrepancy. Meanwhile, to facilitate effective knowledge transfer across graphs, we derive three optimization objectives: (1) the classifier loss to learn discriminative representations; (2) the alignment loss weighted by the graph Wasserstein distance to align the structure and feature distribution; and (3) the pseudo-label loss to refine target node representations. Extensive experiments on real-world datasets confirm that the proposed method outperforms recent state-of-the-art baselines, demonstrating its effectiveness.
Graph rationalization methods aim to improve the explainability of Graph Neural Networks by identifying critical subgraphs (rationales) for task prediction. Motivated by increasing concerns over data privacy, federated graph rationalization has recently gained traction as a novel research area. However, in federated settings, data heterogeneity across clients exacerbates shortcut learning, where models rely on spurious and client-specific features rather than invariant causal rationales. Existing solutions, such as environment-aware data augmentation, suffer from low-quality environment representations. To address this, we propose DiffGR, a Diff erence-based sample selection strategy for federated Graph Rationalization. DiffGR selects samples where local and global models exhibit the highest prediction discrepancies, as these likely reflect strong shortcut reliance, enabling more accurate environment representations. Additionally, we introduce a mutual information (MI) inspired environment-conditioned data augmentation method that minimizes MI between environments and predictions while maximizing MI between rationales and predictions. Experiments on real-world and synthetic datasets demonstrate the effectiveness of DiffGR in improving rationale quality and model robustness in federated settings. Code is available at https://github.com/yuelinan/Codes-of-DiffGR.
Graph distribution shifts between training and test graphs pose severe challenges to the generalization of graph neural networks (GNNs). In real-world deployment, application environments are continuously evolving, while retraining or redesigning GNNs is often costly and impractical. In light of this, test-time adaptation on graphs, which aims to dynamically adapt well-trained GNNs or adjust test graphs to improve inference performance, has attracted growing attention as a practical solution. In this survey, we provide a comprehensive review of test-time adaptation on graphs, an emerging yet underexplored research direction. We identify two fundamental challenges: (1) Data-level: complex graph distribution shifts; and (2) Model-level: limited test-time learning information. Upon this, we present a systematic taxonomy of existing methods into (a) model-centric, (b) data-centric, and (c) hybrid methods, followed by a summary of representative applications, benchmarks, and open opportunities. We aim to bridge the gap between laboratory GNN development and real-world deployment via test-time adaptation. The repository of papers, code, and datasets is at https://github.com/jiayichen1121/Test-Time-Adaptation-for-Graph-Learning.
Graph representation learning (GRL) serves as a canonical paradigm for modeling complex networks. However, real-world AI systems inherently manifest as evolving heterogeneous entities with complex interactions, posing significant challenges to static or homogeneous modeling. To address these complexities, representation learning for Dynamic Heterogeneous Graphs (DHGs) has emerged as a vital approach for learning low-dimensional representations that simultaneously preserve structural semantics and temporal dynamics. This survey presents the first systematic review of DHG representation learning methods. We first introduce a unified formal definition that encompasses both discrete-time and continuous-time DHGs from the perspective of temporal granularity. Building upon this formulation, we propose a novel algorithm-centric taxonomy that categorizes existing literature, including early embedding-based approaches, graph neural network (GNN)-based models, and relatively recent Transformer-based DHG methods, while explicitly highlighting their intrinsic modeling biases with respect to dynamic granularity. Furthermore, we summarize representative applications of DHG representation learning, along with commonly used datasets and benchmarks. Finally, we discuss promising research directions that guide future advances in this rapidly evolving field.
Graphs are a fundamental data structure underlying many problems in the natural and social sciences. Over the past decade, Graph Neural Networks (GNNs) have dominated graph machine learning, supported by solid theoretical foundations. Yet scientists often understand graph structure through vision: chemists read molecular diagrams and social scientists inspect network visualizations. Despite decades of work on graph visualization, most graph learning pipelines still treat graphs purely as symbolic structures, rarely leveraging the visual form of graphs. We argue that this gap deserves renewed attention in the era of powerful vision and vision language models. This survey provides a first systematic overview of the emerging area we term vision meets graphs, which treats visual depictions of graphs as first-class inputs for reasoning and learning. We organize existing work into three threads. Vision for Graph Reasoning studies how models can use visual depictions of graphs to understand structure and carry out multi-step reasoning. Vision for Graph Learning explores how visual features can complement or augment graph encoders beyond known limitations of message passing. Scientific Graphs examines domains where standardized depiction conventions support both reasoning and learning. Our goal is to clarify what current methods can and cannot do, and to outline a path toward foundation models that perceive and reason about graphs as scientists do.
Graph Neural Networks are powerful models for learning from graph-structured data, yet their effectiveness is often limited by two critical challenges: over-squashing, where information from distant nodes is excessively compressed, and over-smoothing, where repeated propagation makes node representations indistinguishable. Both phenomena stem from the interaction between message passing and the input topology, ultimately degrading information flow and limiting the performance of GNNs. In this survey, we examine graph rewiring techniques, a class of methods designed to modify the graph topology to enhance information propagation in GNNs. We provide a comprehensive review of state-of-the-art rewiring approaches, delving into their theoretical underpinnings, practical implementations, and performance trade-offs.