Graph condensation (GC) is an emerging technique designed to learn a significantly smaller graph that retains the essential information of the original graph. This condensed graph has shown promise in accelerating graph neural networks while preserving performance comparable to those achieved with the original, larger graphs. Additionally, this technique facilitates downstream applications like neural architecture search and deepens our understanding of redundancies in large graphs. Despite the rapid development of GC methods, particularly for node classification, a unified evaluation framework is still lacking to systematically compare different GC methods or clarify key design choices for improving their effectiveness. To bridge these gaps, we introduce \textbf{GC4NC}, a comprehensive framework for evaluating diverse GC methods on node classification across multiple dimensions including performance, efficiency, privacy preservation, denoising ability, NAS effectiveness, and transferability. Our systematic evaluation offers novel insights into how condensed graphs behave and the critical design choices that drive their success. These findings pave the way for future advancements in GC methods, enhancing both performance and expanding their real-world applications. Our code is available at https://github.com/Emory-Melody/GraphSlim/tree/main/benchmark.
Graph Neural Networks (GNNs) have been widely used for various learning tasks, ranging from node classification to link prediction. They have demonstrated excellent performance in multiple domains involving graph-structured data. However, an important category of learning tasks, namely link weight prediction, has received less emphasis due to its increased complexity compared to binary link classification. Link weight prediction becomes even more challenging when considering multilayer networks, where nodes can be interconnected across multiple layers. To address these challenges, we propose a new method named Multiplex Spatial Graph Convolution Network (MSGCN), which spatially embeds information across multiple layers to predict interlayer link weights. The MSGCN model generalizes spatial graph convolution to multiplex networks and captures the geometric structure of nodes across multiple layers. Extensive experiments using data with known interlayer link information show that the MSGCN model has robust, accurate, and generalizable link weight prediction performance across a wide variety of multiplex network structures.
Graph neural networks (GNNs) are powerful tools for solving graph-related problems. Distributed GNN frameworks and systems enhance the scalability of GNNs and accelerate model training, yet most are optimized for node classification. Their performance on link prediction remains underexplored. This paper demystifies distributed training of GNNs for link prediction by investigating the issue of performance degradation when each worker trains a GNN on its assigned partitioned subgraph without having access to the entire graph. We discover that the main sources of the issue come from not only the information loss caused by graph partitioning but also the ways of drawing negative samples during model training. While sharing the complete graph information with each worker resolves the issue and preserves link prediction accuracy, it incurs a high communication cost. We propose SpLPG, which effectively leverages graph sparsification to mitigate the issue of performance degradation at a reduced communication cost. Experiment results on several public real-world datasets demonstrate the effectiveness of SpLPG, which reduces the communication overhead by up to about 80% while mostly preserving link prediction accuracy.
Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models capable of generalizing across arbitrary graphs and features? In this work, we present a recipe for designing graph foundation models for node-level tasks from first principles. The key ingredient underpinning our study is a systematic investigation of the symmetries that a graph foundation model must respect. In a nutshell, we argue that label permutation-equivariance alongside feature permutation-invariance are necessary in addition to the common node permutation-equivariance on each local neighborhood of the graph. To this end, we first characterize the space of linear transformations that are equivariant to permutations of nodes and labels, and invariant to permutations of features. We then prove that the resulting network is a universal approximator on multisets that respect the aforementioned symmetries. Our recipe uses such layers on the multiset of features induced by the local neighborhood of the graph to obtain a class of graph foundation models for node property prediction. We validate our approach through extensive experiments on 29 real-world node classification datasets, demonstrating both strong zero-shot empirical performance and consistent improvement as the number of training graphs increases.
Graph Neural Networks (GNNs) have achieved state-of-the-art performance in node classification tasks but struggle with label noise in real-world data. Existing studies on graph learning with label noise commonly rely on class-dependent label noise, overlooking the complexities of instance-dependent noise and falling short of capturing real-world corruption patterns. We introduce BeGIN (Benchmarking for Graphs with Instance-dependent Noise), a new benchmark that provides realistic graph datasets with various noise types and comprehensively evaluates noise-handling strategies across GNN architectures, noisy label detection, and noise-robust learning. To simulate instance-dependent corruptions, BeGIN introduces algorithmic methods and LLM-based simulations. Our experiments reveal the challenges of instance-dependent noise, particularly LLM-based corruption, and underscore the importance of node-specific parameterization to enhance GNN robustness. By comprehensively evaluating noise-handling strategies, BeGIN provides insights into their effectiveness, efficiency, and key performance factors. We expect that BeGIN will serve as a valuable resource for advancing research on label noise in graphs and fostering the development of robust GNN training methods. The code is available at https://github.com/kimsu55/BeGIN.
Message-Passing Neural Networks (MPNNs) have become a cornerstone for processing and analyzing graph-structured data. However, their effectiveness is often hindered by phenomena such as over-squashing, where long-range dependencies or interactions are inadequately captured and expressed in the MPNN output. This limitation mirrors the challenges of the Effective Receptive Field (ERF) in Convolutional Neural Networks (CNNs), where the theoretical receptive field is underutilized in practice. In this work, we show and theoretically explain the limited ERF problem in MPNNs. Furthermore, inspired by recent advances in ERF augmentation for CNNs, we propose an Interleaved Multiscale Message-Passing Neural Networks (IM-MPNN) architecture to address these problems in MPNNs. Our method incorporates a hierarchical coarsening of the graph, enabling message-passing across multiscale representations and facilitating long-range interactions without excessive depth or parameterization. Through extensive evaluations on benchmarks such as the Long-Range Graph Benchmark (LRGB), we demonstrate substantial improvements over baseline MPNNs in capturing long-range dependencies while maintaining computational efficiency.
Graph neural networks (GNNs) has been predominantly driven by message-passing, where node representations are iteratively updated via local neighborhood aggregation. Despite their success, message-passing suffers from fundamental limitations -- including constrained expressiveness, over-smoothing, over-squashing, and limited capacity to model long-range dependencies. These issues hinder scalability: increasing data size or model size often fails to yield improved performance, limiting the viability of GNNs as backbones for graph foundation models. In this work, we explore pathways beyond message-passing and introduce Generative Graph Pattern Machine (G$^2$PM), a generative Transformer pre-training framework for graphs. G$^2$PM represents graph instances (nodes, edges, or entire graphs) as sequences of substructures, and employs generative pre-training over the sequences to learn generalizable, transferable representations. Empirically, G$^2$PM demonstrates strong scalability: on the ogbn-arxiv benchmark, it continues to improve with model sizes up to 60M parameters, outperforming prior generative approaches that plateau at significantly smaller scales (e.g., 3M). In addition, we systematically analyze the model design space, highlighting key architectural choices that contribute to its scalability and generalization. Across diverse tasks -- including node classification, graph classification, and transfer learning -- G$^2$PM consistently outperforms strong baselines, establishing a compelling foundation for scalable graph learning. The code and dataset are available at https://github.com/Zehong-Wang/G2PM.
Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by $k$-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility.
Graph Neural Networks (GNNs) excel at analyzing graph-structured data but struggle on heterophilic graphs, where connected nodes often belong to different classes. While this challenge is commonly addressed with specialized GNN architectures, graph rewiring remains an underexplored strategy in this context. We provide theoretical foundations linking edge homophily, GNN embedding smoothness, and node classification performance, motivating the need to enhance homophily. Building on this insight, we introduce a rewiring framework that increases graph homophily using a reference graph, with theoretical guarantees on the homophily of the rewired graph. To broaden applicability, we propose a label-driven diffusion approach for constructing a homophilic reference graph from node features and training labels. Through extensive simulations, we analyze how the homophily of both the original and reference graphs influences the rewired graph homophily and downstream GNN performance. We evaluate our method on 11 real-world heterophilic datasets and show that it outperforms existing rewiring techniques and specialized GNNs for heterophilic graphs, achieving improved node classification accuracy while remaining efficient and scalable to large graphs.
Counterfactual learning is emerging as an important paradigm, rooted in causality, which promises to alleviate common issues of graph neural networks (GNNs), such as fairness and interpretability. However, as in many real-world application domains where conducting randomized controlled trials is impractical, one has to rely on available observational (factual) data to detect counterfactuals. In this paper, we introduce and tackle the problem of searching for counterfactual evidences for the GNN-based node classification task. A counterfactual evidence is a pair of nodes such that, regardless they exhibit great similarity both in the features and in their neighborhood subgraph structures, they are classified differently by the GNN. We develop effective and efficient search algorithms and a novel indexing solution that leverages both node features and structural information to identify counterfactual evidences, and generalizes beyond any specific GNN. Through various downstream applications, we demonstrate the potential of counterfactual evidences to enhance fairness and accuracy of GNNs.
Graph Neural Networks (GNNs) have become essential for handling large-scale graph applications. However, the computational demands of GNNs necessitate the development of efficient methods to accelerate inference. Mixed precision quantization emerges as a promising solution to enhance the efficiency of GNN architectures without compromising prediction performance. Compared to conventional deep learning architectures, GNN layers contain a wider set of components that can be quantized, including message passing functions, aggregation functions, update functions, the inputs, learnable parameters, and outputs of these functions. In this paper, we introduce a theorem for efficient quantized message passing to aggregate integer messages. It guarantees numerical equality of the aggregated messages using integer values with respect to those obtained with full (FP32) precision. Based on this theorem, we introduce the Mixed Precision Quantization for GNN (MixQ-GNN) framework, which flexibly selects effective integer bit-widths for all components within GNN layers. Our approach systematically navigates the wide set of possible bit-width combinations, addressing the challenge of optimizing efficiency while aiming at maintaining comparable prediction performance. MixQ-GNN integrates with existing GNN quantization methods, utilizing their graph structure advantages to achieve higher prediction performance. On average, MixQ-GNN achieved reductions in bit operations of 5.5x for node classification and 5.1x for graph classification compared to architectures represented in FP32 precision.
Nowadays, numerous online platforms can be described as multi-modal heterogeneous networks (MMHNs), such as Douban's movie networks and Amazon's product review networks. Accurately categorizing nodes within these networks is crucial for analyzing the corresponding entities, which requires effective representation learning on nodes. However, existing multi-modal fusion methods often adopt either early fusion strategies which may lose the unique characteristics of individual modalities, or late fusion approaches overlooking the cross-modal guidance in GNN-based information propagation. In this paper, we propose a novel model for node classification in MMHNs, named Heterogeneous Graph Neural Network with Inter-Modal Attention (HGNN-IMA). It learns node representations by capturing the mutual influence of multiple modalities during the information propagation process, within the framework of heterogeneous graph transformer. Specifically, a nested inter-modal attention mechanism is integrated into the inter-node attention to achieve adaptive multi-modal fusion, and modality alignment is also taken into account to encourage the propagation among nodes with consistent similarities across all modalities. Moreover, an attention loss is augmented to mitigate the impact of missing modalities. Extensive experiments validate the superiority of the model in the node classification task, providing an innovative view to handle multi-modal data, especially when accompanied with network structures.
Effective and efficient graph representation learning is essential for enabling critical downstream tasks, such as node classification, link prediction, and subgraph search. However, existing graph neural network (GNN) architectures often struggle to adapt to diverse and complex graph structures, limiting their ability to produce structure-aware and task-discriminative representations. To address this challenge, we propose ABG-NAS, a novel framework for automated graph neural network architecture search tailored for efficient graph representation learning. ABG-NAS encompasses three key components: a Comprehensive Architecture Search Space (CASS), an Adaptive Genetic Optimization Strategy (AGOS), and a Bayesian-Guided Tuning Module (BGTM). CASS systematically explores diverse propagation (P) and transformation (T) operations, enabling the discovery of GNN architectures capable of capturing intricate graph characteristics. AGOS dynamically balances exploration and exploitation, ensuring search efficiency and preserving solution diversity. BGTM further optimizes hyperparameters periodically, enhancing the scalability and robustness of the resulting architectures. Empirical evaluations on benchmark datasets (Cora, PubMed, Citeseer, and CoraFull) demonstrate that ABG-NAS consistently outperforms both manually designed GNNs and state-of-the-art neural architecture search (NAS) methods. These results highlight the potential of ABG-NAS to advance graph representation learning by providing scalable and adaptive solutions for diverse graph structures. Our code is publicly available at https://github.com/sserranw/ABG-NAS.
Graph Transformers (GTs) have shown advantages in numerous graph structure tasks but their self-attention mechanism ignores the generalization bias of graphs, with existing methods mainly compensating for this bias from aspects like position encoding, attention bias and relative distance yet still having sub-optimal performance and being insufficient by only considering the structural perspective of generalization bias. To address this, this paper proposes Grafourierformer, which innovatively combines GT with inductive bias containing Frequency-Structure information by applying Graph Fourier Transform to the Attention Matrix: specifically, eigenvalues from the Graph Laplacian matrix are used to construct an Eigenvalue matrix mask (reflecting node positions and structural relationships with neighboring nodes to enable consideration of node range structural characteristics and focus on local graph details), and inverse Fourier transform is employed to extract node high-frequency and low-frequency features, calculate low-frequency and high-frequency energy, and construct a node frequency-energy matrix to filter the eigenvalue matrix mask, allowing attention heads to incorporate both graph structural information and node frequency information optimization, adaptively distinguish global trends from local details, and effectively suppress redundant information interference. Extensive experiments on various benchmarks show Grafourierformer consistently outperforms GNN and GT-based models in graph classification and node classification tasks, with ablation experiments further validating the effectiveness and necessity of the method. Codes are available at https://github.com/Arichibald/Grafourierformer.git
Wide & Deep, a simple yet effective learning architecture for recommendation systems developed by Google, has had a significant impact in both academia and industry due to its combination of the memorization ability of generalized linear models and the generalization ability of deep models. Graph convolutional networks (GCNs) remain dominant in node classification tasks; however, recent studies have highlighted issues such as heterophily and expressiveness, which focus on graph structure while seemingly neglecting the potential role of node features. In this paper, we propose a flexible framework GCNIII, which leverages the Wide & Deep architecture and incorporates three techniques: Intersect memory, Initial residual and Identity mapping. We provide comprehensive empirical evidence showing that GCNIII can more effectively balance the trade-off between over-fitting and over-generalization on various semi- and full- supervised tasks. Additionally, we explore the use of large language models (LLMs) for node feature engineering to enhance the performance of GCNIII in cross-domain node classification tasks. Our implementation is available at https://github.com/CYCUCAS/GCNIII.
Self-supervised learning (SSL) in graphs has garnered significant attention, particularly in employing Graph Neural Networks (GNNs) with pretext tasks initially designed for other domains, such as contrastive learning and feature reconstruction. However, it remains uncertain whether these methods effectively reflect essential graph properties, precisely representation similarity with its neighbors. We observe that existing methods position opposite ends of a spectrum driven by the graph embedding smoothness, with each end corresponding to outperformance on specific downstream tasks. Decomposing the SSL objective into three terms via an information-theoretic framework with a neighbor representation variable reveals that this polarization stems from an imbalance among the terms, which existing methods may not effectively maintain. Further insights suggest that balancing between the extremes can lead to improved performance across a wider range of downstream tasks. A framework, BSG (Balancing Smoothness in Graph SSL), introduces novel loss functions designed to supplement the representation quality in graph-based SSL by balancing the derived three terms: neighbor loss, minimal loss, and divergence loss. We present a theoretical analysis of the effects of these loss functions, highlighting their significance from both the SSL and graph smoothness perspectives. Extensive experiments on multiple real-world datasets across node classification and link prediction consistently demonstrate that BSG achieves state-of-the-art performance, outperforming existing methods. Our implementation code is available at https://github.com/steve30572/BSG.
Graph Transformers (GTs), which simultaneously integrate message-passing and self-attention mechanisms, have achieved promising empirical results in some graph prediction tasks. Although these approaches show the potential of Transformers in capturing long-range graph topology information, issues concerning the quadratic complexity and high computing energy consumption severely limit the scalability of GTs on large-scale graphs. Recently, as brain-inspired neural networks, Spiking Neural Networks (SNNs), facilitate the development of graph representation learning methods with lower computational and storage overhead through the unique event-driven spiking neurons. Inspired by these characteristics, we propose a linear-time Graph Transformer using Spiking Vector Quantization (GT-SVQ) for node classification. GT-SVQ reconstructs codebooks based on rate coding outputs from spiking neurons, and injects the codebooks into self-attention blocks to aggregate global information in linear complexity. Besides, spiking vector quantization effectively alleviates codebook collapse and the reliance on complex machinery (distance measure, auxiliary loss, etc.) present in previous vector quantization-based graph learning methods. In experiments, we compare GT-SVQ with other state-of-the-art baselines on node classification datasets ranging from small to large. Experimental results show that GT-SVQ has achieved competitive performances on most datasets while maintaining up to 130x faster inference speed compared to other GTs.
Graph self-supervised learning has gained significant attention recently. However, many existing approaches heavily depend on perturbations, and inappropriate perturbations may corrupt the graph's inherent information. The Vector Quantized Variational Autoencoder (VQ-VAE) is a powerful autoencoder extensively used in fields such as computer vision; however, its application to graph data remains underexplored. In this paper, we provide an empirical analysis of vector quantization in the context of graph autoencoders, demonstrating its significant enhancement of the model's capacity to capture graph topology. Furthermore, we identify two key challenges associated with vector quantization when applying in graph data: codebook underutilization and codebook space sparsity. For the first challenge, we propose an annealing-based encoding strategy that promotes broad code utilization in the early stages of training, gradually shifting focus toward the most effective codes as training progresses. For the second challenge, we introduce a hierarchical two-layer codebook that captures relationships between embeddings through clustering. The second layer codebook links similar codes, encouraging the model to learn closer embeddings for nodes with similar features and structural topology in the graph. Our proposed model outperforms 16 representative baseline methods in self-supervised link prediction and node classification tasks across multiple datasets.
Text-attributed graphs (TAGs) present unique challenges in representation learning by requiring models to capture both the semantic richness of node-associated texts and the structural dependencies of the graph. While graph neural networks (GNNs) excel at modeling topological information, they lack the capacity to process unstructured text. Conversely, large language models (LLMs) are proficient in text understanding but are typically unaware of graph structure. In this work, we propose BiGTex (Bidirectional Graph Text), a novel architecture that tightly integrates GNNs and LLMs through stacked Graph-Text Fusion Units. Each unit allows for mutual attention between textual and structural representations, enabling information to flow in both directions, text influencing structure and structure guiding textual interpretation. The proposed architecture is trained using parameter-efficient fine-tuning (LoRA), keeping the LLM frozen while adapting to task-specific signals. Extensive experiments on five benchmark datasets demonstrate that BiGTex achieves state-of-the-art performance in node classification and generalizes effectively to link prediction. An ablation study further highlights the importance of soft prompting and bi-directional attention in the model's success.
Temporal Graph Networks (TGNs) have demonstrated significant success in dynamic graph tasks such as link prediction and node classification. Both tasks comprise transductive settings, where the model predicts links among known nodes, and in inductive settings, where it generalises learned patterns to previously unseen nodes. Existing TGN designs face a dilemma under these dual scenarios. Anonymous TGNs, which rely solely on temporal and structural information, offer strong inductive generalisation but struggle to distinguish known nodes. In contrast, non-anonymous TGNs leverage node features to excel in transductive tasks yet fail to adapt to new nodes. To address this challenge, we propose Trajectory Encoding TGN (TETGN). Our approach introduces automatically expandable node identifiers (IDs) as learnable temporal positional features and performs message passing over these IDs to capture each node's historical context. By integrating this trajectory-aware module with a standard TGN using multi-head attention, TETGN effectively balances transductive accuracy with inductive generalisation. Experimental results on three real-world datasets show that TETGN significantly outperforms strong baselines on both link prediction and node classification tasks, demonstrating its ability to unify the advantages of anonymous and non-anonymous models for dynamic graph learning.