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
Federated Graph Learning (FGL) empowers clients to collaboratively train Graph neural networks (GNNs) in a distributed manner while preserving data privacy. However, FGL methods usually require that the graph data owned by all clients is homophilic to ensure similar neighbor distribution patterns of nodes. Such an assumption ensures that the learned knowledge is consistent across the local models from all clients. Therefore, these local models can be properly aggregated as a global model without undermining the overall performance. Nevertheless, when the neighbor distribution patterns of nodes vary across different clients (e.g., when clients hold graphs with different levels of heterophily), their local models may gain different and even conflict knowledge from their node-level predictive tasks. Consequently, aggregating these local models usually leads to catastrophic performance deterioration on the global model. To address this challenge, we propose FedHERO, an FGL framework designed to harness and share insights from heterophilic graphs effectively. At the heart of FedHERO is a dual-channel GNN equipped with a structure learner, engineered to discern the structural knowledge encoded in the local graphs. With this specialized component, FedHERO enables the local model for each client to identify and learn patterns that are universally applicable across graphs with different patterns of node neighbor distributions. FedHERO not only enhances the performance of individual client models by leveraging both local and shared structural insights but also sets a new precedent in this field to effectively handle graph data with various node neighbor distribution patterns. We conduct extensive experiments to validate the superior performance of FedHERO against existing alternatives.
Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recently, a few works have extended fairness to graph data, such as social networks, but most of them neglect the causal relationships among data instances. This paper addresses the prevalent challenge in fairness-aware ML algorithms, which typically assume Independent and Identically Distributed (IID) data. We tackle the overlooked domain of non-IID, graph-based settings where data instances are interconnected, influencing the outcomes of fairness interventions. We base our research on the Network Structural Causal Model (NSCM) framework and posit two main assumptions: Decomposability and Graph Independence, which enable the computation of interventional distributions in non-IID settings using the $do$-calculus. Based on that, we develop the Message Passing Variational Autoencoder for Causal Inference (MPVA) to compute interventional distributions and facilitate causally fair node classification through estimated interventional distributions. Empirical evaluations on semi-synthetic and real-world datasets demonstrate that MPVA outperforms conventional methods by effectively approximating interventional distributions and mitigating bias. The implications of our findings underscore the potential of causality-based fairness in complex ML applications, setting the stage for further research into relaxing the initial assumptions to enhance model fairness.
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.
Graph auto-encoder is considered a framework for unsupervised learning on graph-structured data by representing graphs in a low dimensional space. It has been proved very powerful for graph analytics. In the real world, complex relationships in various entities can be represented by heterogeneous graphs that contain more abundant semantic information than homogeneous graphs. In general, graph auto-encoders based on homogeneous graphs are not applicable to heterogeneous graphs. In addition, little work has been done to evaluate the effect of different semantics on node embedding in heterogeneous graphs for unsupervised graph representation learning. In this work, we propose a novel Heterogeneous Graph Attention Auto-Encoders (HGATE) for unsupervised representation learning on heterogeneous graph-structured data. Based on the consideration of semantic information, our architecture of HGATE reconstructs not only the edges of the heterogeneous graph but also node attributes, through stacked encoder/decoder layers. Hierarchical attention is used to learn the relevance between a node and its meta-path based neighbors, and the relevance among different meta-paths. HGATE is applicable to transductive learning as well as inductive learning. Node classification and link prediction experiments on real-world heterogeneous graph datasets demonstrate the effectiveness of HGATE for both transductive and inductive tasks.
Graph Neural Networks (GNNs) update node representations through message passing, which is primarily based on the homophily principle, assuming that adjacent nodes share similar features. However, in real-world graphs with long-tailed degree distributions, high-degree nodes dominate message passing, causing a degree bias where low-degree nodes remain under-represented due to inadequate messages. The main challenge in addressing degree bias is how to discover non-adjacent nodes to provide additional messages to low-degree nodes while reducing excessive messages for high-degree nodes. Nevertheless, exploiting non-adjacent nodes to provide valuable messages is challenging, as it could generate noisy information and disrupt the original graph structures. To solve it, we propose a novel Degree Fairness Graph Transformer, named DegFairGT, to mitigate degree bias by discovering structural similarities between non-adjacent nodes through learnable structural augmentation and structural self-attention. Our key idea is to exploit non-adjacent nodes with similar roles in the same community to generate informative edges under our augmentation, which could provide informative messages between nodes with similar roles while ensuring that the homophily principle is maintained within the community. To enable DegFairGT to learn such structural similarities, we then propose a structural self-attention to capture the similarities between node pairs. To preserve global graph structures and prevent graph augmentation from hindering graph structure, we propose a Self-Supervised Learning task to preserve p-step transition probability and regularize graph augmentation. Extensive experiments on six datasets showed that DegFairGT outperformed state-of-the-art baselines in degree fairness analysis, node classification, and node clustering tasks.
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.
Federated Graph Learning (FGL) enables privacy-preserving, distributed training of graph neural networks without sharing raw data. Among its approaches, subgraph-FL has become the dominant paradigm, with most work focused on improving overall node classification accuracy. However, these methods often overlook fairness due to the complexity of node features, labels, and graph structures. In particular, they perform poorly on nodes with disadvantaged properties, such as being in the minority class within subgraphs or having heterophilous connections (neighbors with dissimilar labels or misleading features). This reveals a critical issue: high accuracy can mask degraded performance on structurally or semantically marginalized nodes. To address this, we advocate for two fairness goals: (1) improving representation of minority class nodes for class-wise fairness and (2) mitigating topological bias from heterophilous connections for topology-aware fairness. We propose FairFGL, a novel framework that enhances fairness through fine-grained graph mining and collaborative learning. On the client side, the History-Preserving Module prevents overfitting to dominant local classes, while the Majority Alignment Module refines representations of heterophilous majority-class nodes. The Gradient Modification Module transfers minority-class knowledge from structurally favorable clients to improve fairness. On the server side, FairFGL uploads only the most influenced subset of parameters to reduce communication costs and better reflect local distributions. A cluster-based aggregation strategy reconciles conflicting updates and curbs global majority dominance . Extensive evaluations on eight benchmarks show FairFGL significantly improves minority-group performance , achieving up to a 22.62 percent Macro-F1 gain while enhancing convergence over state-of-the-art baselines.
Graphs are growing rapidly, along with the number of distinct label categories associated with them. Applications like e-commerce, healthcare, recommendation systems, and various social media platforms are rapidly moving towards graph representation of data due to their ability to capture both structural and attribute information. One crucial task in graph analysis is node classification, where unlabeled nodes are categorized into predefined classes. In practice, novel classes appear incrementally sometimes with just a few labels (seen classes) or even without any labels (unseen classes), either because they are new or haven't been explored much. Traditional methods assume abundant labeled data for training, which isn't always feasible. We investigate a broader objective: \emph{Graph Class Incremental Learning under Weak Supervision (GCL)}, addressing this challenge by meta-training on base classes with limited labeled instances. During the incremental streams, novel classes can have few-shot or zero-shot representation. Our proposed framework GOTHAM efficiently accommodates these unlabeled nodes by finding the closest prototype representation, serving as class representatives in the attribute space. For Text-Attributed Graphs (TAGs), our framework additionally incorporates semantic information to enhance the representation. By employing teacher-student knowledge distillation to mitigate forgetting, GOTHAM achieves promising results across various tasks. Experiments on datasets such as Cora-ML, Amazon, and OBGN-Arxiv showcase the effectiveness of our approach in handling evolving graph data under limited supervision. The repository is available here: \href{https://github.com/adityashahane10/GOTHAM--Graph-based-Class-Incremental-Learning-Framework-under-Weak-Supervision}{\small \textcolor{blue}{Code}}
The rapid growth in the size of Graph Convolutional Neural Networks (GCNs) encounters both computational- and memory-wall on classical computing platforms (e.g., CPU, GPU, FPGA, etc.). Quantum computing, on the other hand, provides extremely high parallelism for computation. Although quantum neural networks have been recently studied, the research on quantum graph neural networks is still in its infancy. The key challenge here is how to integrate both the graph topology information and the learning ability of GCNs into quantum circuits. In this work, we leverage the Givens rotations and its quantum implementation to encode graph information; in addition, we employ the widely used variational quantum circuit to bring the learnable parameters. On top of these, we present a full-quantum design of Graph Convolutional Neural Networks, namely "QuGCN", for semi-supervised learning on graph-structured data. Experiment results show our design is competitive with classical GCNs in terms of node classification accuracy on Cora sub-dataset. More importantly, we show the potential advantages that can be achieved by the proposed quantum GCN design when the number of features grows.
Graph Neural Networks (GNNs) have emerged as the de facto standard for modeling graph data, with attention mechanisms and transformers significantly enhancing their performance on graph-based tasks. Despite these advancements, the performance of GNNs on heterogeneous graphs often remains complex, with networks generally underperforming compared to their homogeneous counterparts. This work benchmarks various GNN architectures to identify the most effective methods for heterogeneous graphs, with a particular focus on node classification and link prediction. Our findings reveal that graph attention networks excel in these tasks. As a main contribution, we explore enhancements to these attention networks by integrating positional encodings for node embeddings. This involves utilizing the full Laplacian spectrum to accurately capture both the relative and absolute positions of each node within the graph, further enhancing performance on downstream tasks such as node classification and link prediction.
In this paper, we propose a novel \emph{uncertainty-aware graph self-training} approach for semi-supervised node classification. Our method introduces an Expectation-Maximization (EM) regularization scheme to incorporate an uncertainty mechanism during pseudo-label generation and model retraining. Unlike conventional graph self-training pipelines that rely on fixed pseudo-labels, our approach iteratively refines label confidences with an EM-inspired uncertainty measure. This ensures that the predictive model focuses on reliable graph regions while gradually incorporating ambiguous nodes. Inspired by prior work on uncertainty-aware self-training techniques~\cite{wang2024uncertainty}, our framework is designed to handle noisy graph structures and feature spaces more effectively. Through extensive experiments on several benchmark graph datasets, we demonstrate that our method outperforms strong baselines by a margin of up to 2.5\% in accuracy while maintaining lower variance in performance across multiple runs.
Self-training has become a popular semi-supervised learning technique for leveraging unlabeled data. However, the over-confidence of pseudo-labels remains a key challenge. In this paper, we propose a novel \emph{graph-based uncertainty-aware self-training} (GUST) framework to combat over-confidence in node classification. Drawing inspiration from the uncertainty integration idea introduced by Wang \emph{et al.}~\cite{wang2024uncertainty}, our method largely diverges from previous self-training approaches by focusing on \emph{stochastic node labeling} grounded in the graph topology. Specifically, we deploy a Bayesian-inspired module to estimate node-level uncertainty, incorporate these estimates into the pseudo-label generation process via an expectation-maximization (EM)-like step, and iteratively update both node embeddings and adjacency-based transformations. Experimental results on several benchmark graph datasets demonstrate that our GUST framework achieves state-of-the-art performance, especially in settings where labeled data is extremely sparse.
Node classification in graphs aims to predict the categories of unlabeled nodes by utilizing a small set of labeled nodes. However, weighted graphs often contain noisy edges and anomalous edge weights, which can distort fine-grained relationships between nodes and hinder accurate classification. We propose the Edge Weight-aware Graph Structure Learning (EWGSL) method, which combines weight learning and graph structure learning to address these issues. EWGSL improves node classification by redefining attention coefficients in graph attention networks to incorporate node features and edge weights. It also applies graph structure learning to sparsify attention coefficients and uses a modified InfoNCE loss function to enhance performance by adapting to denoised graph weights. Extensive experimental results show that EWGSL has an average Micro-F1 improvement of 17.8% compared with the best baseline.
Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods have been proposed to capture structural proximity among nodes in a network, where densely connected communities are preserved, while others have been proposed to preserve structural equivalence among nodes, capturing their structural roles regardless of their relative distance in the network. However, most existing methods that aim to preserve both network characteristics mainly focus on static networks and those designed for dynamic networks do not explicitly account for inter-snapshot structural properties. This paper proposes a novel unifying dynamic network embedding method that simultaneously preserves both structural proximity and equivalence while considering inter-snapshot structural relationships in a dynamic network. Specifically, to define structural equivalence in a dynamic network, we use temporal subgraphs, known as dynamic graphlets, to capture how a node's neighborhood structure evolves over time. We then introduce a temporal-structural random walk to flexibly sample time-respecting sequences of nodes, considering both their temporal proximity and similarity in evolving structures. The proposed method is evaluated using five real-world networks on node classification where it outperforms benchmark methods, showing its effectiveness and flexibility in capturing various aspects of a network.