Hypergraphs are the natural description of higher-order interactions among objects, widely applied in social network analysis, cross-modal retrieval, etc. Hypergraph Neural Networks (HGNNs) have become the dominant solution for learning on hypergraphs. Traditional HGNNs are extended from message passing graph neural networks, following the homophily assumption, and thus struggle with the prevalent heterophilic hypergraphs that call for long-range dependence modeling. Existing solutions enlarge the message flow through the hypergraph bottleneck, mitigating the oversquashing issue and capturing long-range dependence. However, they often accelerate the loss of representation distinguishability in the repeated aggregations, leading to oversmoothing. This dilemma motivates an interesting question: Can we develop a unified mechanism that is agnostic to both homophilic and heterophilic hypergraphs? In this paper, we achieve the best of both worlds through the lens of Riemannian geometry, which provides the potential to adjust the message passing behavior in different regions. The key insight lies in the connection between oversquashing and hypergraph bottleneck within the framework of Riemannian manifold heat flow. Building on this, we propose the novel idea of locally adapting the bottlenecks of different subhypergraphs. The core innovation of the proposed mechanism is the design of an adaptive local (heat) exchanger. Specifically, it captures the rich long-range dependencies via the Robin condition, and preserves the representation distinguishability via source terms, thereby enabling heterophily-agnostic message passing with theoretical guarantees. Based on this theoretical foundation, we present a novel Heat-Exchanger with Adaptive Locality for Hypergraph Neural Network (HealHGNN), designed as a node-hyperedge bidirectional systems with linear complexity in the number of nodes and hyperedges. Extensive experiments on both homophilic and heterophilic cases show that HealHGNN achieves the state-of-the-art performance.
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Contrastive learning has demonstrated strong performance in attributed hypergraph clustering. Typically, existing methods based on contrastive learning first learn node embeddings and then apply clustering algorithms, such as k-means, to these embeddings to obtain the clustering results.However, these methods lack direct clustering supervision, risking the inclusion of clustering-irrelevant information in the learned graph. To this end, we propose a Contrastive learning approach for Attributed Hypergraph Clustering (CAHC), an end-to-end method that simultaneously learns node embeddings and obtains clustering results. CAHC consists of two main steps: representation learning and cluster assignment learning. The former employs a novel contrastive learning approach that incorporates both node-level and hyperedge-level objectives to generate node embeddings.The latter joint embedding and clustering optimization to refine these embeddings by clustering-oriented guidance and obtains clustering results simultaneously.Extensive experimental results demonstrate that CAHC outperforms baselines on eight datasets.
Anomalous graphs, representing rare but critical deviations from normal graphs, frequently arise in high-stakes domains such as malicious website detection. Detecting them is highly challenging due to two key issues: (i) labeled anomalous graphs are extremely limited and fail to capture the diversity of real-world abnormality, restricting detection models from generalizing to unseen anomalies encountered in the open world, and (ii) normal graphs often contain spurious or atypical substructures that do not indicate anomalies but may induce models to misclassify normal variations as anomalies. To tackle these challenges, we propose G-GLAD, a generalizable graph-level anomaly detection framework. G-GLAD introduces two key innovations: (1) prompt-based anomaly space expansion, which injects learnable prompts into the graph representation process of known anomalies to simulate diverse unseen anomalous variants. This allows the model to learn a richer and more generalizable anomaly space; and (2) subgraph-based normality extraction, guided by the Information Bottleneck Principle, which isolates essential substructures for normality prediction while filtering out spurious motifs, improving robustness against structural noise. We conduct extensive experiments on ten real-world graph datasets under different empirical settings. The results demonstrate that G-GLAD achieves superior performance and generalizability in identifying anomalous graphs.
Graph Neural Networks (GNNs) have become the dominant paradigm for machine learning on relational data, yet they remain susceptible to overfitting and noise in graph structures. While data augmentation has proven effective for regularization across domains, existing graph methods operate at coarse levels, such as perturbing entire structures or mixing node features. These approaches are context-agnostic and do not target the core computational process of GNNs: message passing. We introduce MessageShift, a novel fine-grained data augmentation paradigm that operates directly on the messages, the atomic units of information, as they flow through the GNN. The core idea is to apply a contextual perturbation to each message by shifting it towards or away from the center of its local neighborhood. This provides a rich regularization effect, capable of both smoothing noisy messages and sharpening distinctive ones. Extensive experiments on a wide range of benchmark datasets demonstrate that MessageShift consistently outperforms strong baselines across multiple GNN backbones.
Multi-Graph Learning (MGL) is a fundamental machine learning paradigm that represents objects as bags-of-graphs, each encoding a distinct structural property, and has broad applications in bioinformatics, chemistry, computing power networks, and software defect detection. However, the inherent scarcity of labeled data poses a significant bottleneck for supervised MGL approaches. While self-supervised contrastive learning offers a compelling solution, its direct application to MGL faces three key challenges: (1) existing graph neural networks, primarily for single-graph modeling, struggle to yield discriminative bag-level representations from bags-of-graphs; (2) conventional contrastive objectives are limited to single-level settings, failing to capture cross-hierarchical dependencies; and (3) standard data augmentation often disrupts intrinsic graph and bag structures, undermining semantic consistency. To address these issues, we propose the Hierarchical Graph-Bag-Network (HGBN), a self-supervised MGL framework that constructs hierarchical representations in the form of a graph-bag-network. HGBN employs an asymmetric hierarchical graph neural network to learn discriminative graph-level and bag-level representations, introduces cross-hierarchical contrastive objectives to align graph-level and bag-level semantics, and leverages the asymmetric network outputs to form positive and negative pairs, preserving intrinsic structural and semantic consistency. Experiments on eight benchmark multi-graph datasets demonstrate that HGBN consistently outperforms both supervised and self-supervised state-of-the-art baselines, achieving average improvements of 4.82% in accuracy and F1 score.
Defending against backdoor attacks on graphs has become increasingly critical. Existing methods predominantly focus on detecting and removing triggers by identifying inconsistencies between trigger and clean nodes. However, adversaries can design triggers that closely resemble clean nodes, making them challenging to detect. Therefore, understanding the mechanisms underlying backdoor attacks is crucial. In this work, we observe an interesting phenomenon: in backdoored models, specific ''backdoor neurons'' (embedding dimensions) are more likely to be activated, causing nodes to be misclassified to the target label. This is largely due to the graph structure, where malicious information propagates through node neighborhoods, activating specific neurons and target label. Based on this observation, we theoretically and empirically demonstrate how graph backdoor attacks exploit this propagation mechanism to effectively poison the target node's embedding. Meanwhile, we propose a novel defense called Graph Backdoor Neuron Defense (GBND) to identify, unlearn, and recover backdoor neurons. Specifically, we design a novel reverse engineering technique to identify triggers that activate backdoor neurons, and eliminate their harmful effects by asymmetric unlearning and recovering at the neuron level. Extensive experiments on four datasets validate the effectiveness of GBND in defending against backdoor attacks.
This paper investigates a novel and critical problem of Graph Cross-Domain Continual Fine-Tuning, which aims to adapt a large pre-trained Graph Foundation Model across diverse domains. Existing continual graph learning methods are mostly limited to incremental settings within only a single domain, and are typically trained from scratch. As a result, they fail to handle cross-domain shifts effectively, suffer from severe forgetting, and lack transferability. To address these challenges, we present G-CORMoL, Graph Continual Fine-tuning with Orthogonal, Router-driven Mixture of LoRA experts. G-CORMoL achieves effective adaptation while preserving prior knowledge by enforcing mathematical orthogonality between expert LoRA adapters, thereby eliminating interference across tasks. It further supports cross-domain knowledge transfer through a symmetric dual-driven routing mechanism that learns a global composition policy over all learned LoRA experts. In addition, it promotes expert specialization via a contrastive objective with theoretical guarantees. Extensive experiments on different cross-domain task orders demonstrate that G-CORMoL achieves robust state-of-the-art performance, not only preventing catastrophic forgetting but also leveraging accumulated knowledge to enable positive transfer.
Graph Anomaly Detection (GAD) is critical in applications such as fraud prevention, cybersecurity, and social governance. While Graph Neural Networks (GNNs) have achieved remarkable success in detecting anomalies on homogeneous graphs, they face fundamental challenges in real-world heterogeneous settings involving diverse node types and imbalanced semantic richness. In heterogeneous graphs, nodes often vary significantly in semantic richness, with anomalies potentially spanning multiple types and emerging implicitly through cross-type dependencies. We identify two core limitations of existing methods: (i) the ineffective propagation of discriminative anomaly cues from informative to sparse nodes due to semantic imbalance, and (ii) conflicting optimization objectives arising from joint detection across multiple node types. To address these issues, we propose CSA-MTHGAD, a novel framework that integrates smoothness-guided cross-type semantic alignment with dynamic multi-task learning. It selectively propagates anomaly-sensitive features across types and harmonizes task-specific gradients through adaptive projection and weighting.To facilitate research, we employ two real-world heterogeneous benchmarks in the domain of social governance. Extensive experiments demonstrate that CSA-MTHGAD achieves superior performance over state-of-the-art baselines in accuracy, robustness, and generalization for multi-type anomaly detection.
Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in graph clustering tasks faces two critical challenges. (1) The introduction of edge weights may significantly increase storage space and training time, making it essential to reduce the graph scale while preserving nodes that are beneficial for the clustering task. (2) Edge weight information may inherently contain noise that negatively impacts clustering results. However, few studies can jointly optimize clustering and edge weights, which is crucial for mitigating the negative impact of noisy edges on clustering task. To address these challenges, we propose a contractile edge-weight-aware graph clustering network. Specifically, a cluster-oriented graph contraction module is designed to reduce the graph scale while preserving important nodes. An edge-weight-aware attention network is designed to identify and weaken noisy connections. In this way, we can more easily identify and mitigate the impact of noisy edges during the clustering process, thus enhancing clustering effectiveness. We conducted extensive experiments on three real-world weighted graph datasets. In particular, our model outperforms the best baseline, demonstrating its superior performance. Furthermore, experiments also show that the proposed graph contraction module can significantly reduce training time and storage space.
Social event detection (SED) enhances public awareness by clustering large-scale social messages and has been widely applied across diverse domains. While many existing frameworks adopt Graph Convolution Networks (GCN) as backbones and extend them with auxiliary modules to model complex message relationships, they rarely explore the deeper potential of GCN itself. Specifically, the core operation of GCN—smoothed feature aggregation—implicitly assumes that social information diffusion follows a single-pass and independent heat propagation process. However, real-world diffusion is inherently multi-wave and oscillatory, where different messages interact through reinforcement and interference, resembling the principle of wave–particle duality. To address this gap, we propose Physics-Inspired Graph Convolution Networks (PIGCN ), a novel model that unifies wave-based propagation and particle-like interactions. Specifically, PIGCN integrates a Helmholtz Graph Filter module to capture spectral wave propagation with oscillatory dynamics, and a Physical Interaction Force mechanism to adaptively adjust edge weights by attracting messages within the same event and repelling those across events. Building on PIGCN, we further incorporate a contextualized text encoder and timestamp encoding to form a comprehensive SED framework. Extensive experiments demonstrate that PIGCN effectively outperforms conventional GCN baselines and achieves superior performance across multiple SED datasets, establishing a new benchmark for balancing architectural simplicity with effectiveness. Our code can be found on GitHub . https://github.com/yuyongsheng1990/PIGCN
Graph Neural Networks (GNNs) have demonstrated impressive performance across diverse graph-based tasks by leveraging message passing to capture complex node relationships. However, on large-scale real-world graphs, GNNs face two major challenges: (1) GNNs struggle to ensure scalability and efficiency as repeated aggregation of large neighborhoods incurs significant computational overhead; (2) GNNs suffer from over-smoothing, where excessive propagation makes node representations indistinguishable, hindering model expressiveness. To tackle these, we propose ScaleGNN, which adaptively fuses multi-hop node features for scalable and effective graph learning. We first compute per-hop pure-neighbor matrices to isolate exclusive structural signals, then apply lightweight fusion to balance low- and high-order information, preserving both local detail and global correlations. To curb redundancy and over-smoothing, we introduce Local Contribution Score (LCS)–based masking to prune low-relevance high-order neighbors, and impose learnable sparsity to selectively integrate valuable multi-hop features. Extensive experiments on real-world datasets show that ScaleGNN consistently outperforms state-of-the-art GNNs in both predictive accuracy and computational efficiency. The source code is available at https://github.com/lx970414/ScaleGNN.
The out-of-distribution (OOD) generalization of graph neural networks poses significant challenges in Web applications, where data resides in complex heterogeneous information networks. Such networks exhibit not only structural heterogeneity but also distribution shifts arising from evolving user behaviors and data collection biases. Conventional GNNs often struggle to identify stable patterns in such heterogeneous graphs, particularly in the absence of explicit environment labels. The core issue is that latent environments can create spurious correlations between node features, local topology, and labels. Models may then rely on these environment-specific shortcuts for predictions, failing to learn the invariant mechanisms that generalize under distribution shifts. To address these limitations, we propose InvHG (Invariant Learning on Heterogeneous Graphs via Subgraph Environment Inference), a causality-inspired framework that infers latent environments at the subgraph level, disentangles type-specific confounding effects, and leverages regularized expert fusion to learn invariant representations. Extensive experiments on heterogeneous graph OOD benchmarks demonstrate that InvHG consistently outperforms state-of-the-art methods, offering a robust solution for complex Web graph learning. The source code is available at https://github.com/mok630/InvHG.
Semi-supervised graph anomaly detection confronts the fundamental challenge of identifying anomalous nodes that exhibit deviations from normal graph patterns in node attributes or structure connectivity, using a small set of labeled normal nodes. Existing methods fall short in modeling the spectrum of anomaly severity, as they generate anomalies in a single, undifferentiated step. This oversight restricts the detection of complex anomalies. In this paper, we propose a progressive anomaly generation network (PAGE) to overcome this limitation. PAGE enhances complex anomaly detection through progressive attribute-structure perturbation: It first injects attribute noise into selected normal nodes to generate pseudo-anomalous nodes. Then it applies progressive structure perturbation to create hybrid anomalies that simulate the evolution from mild to complex perturbations. Importantly, the proposed anomaly progressive constraint loss enforces that hybrid anomalies exhibit a higher degree of abnormality than primary anomalies, enhancing the model's anomaly quantification capability. PAGE further integrates deviation constraint loss and classification loss to optimize node representations and improve prediction. Extensive experiments on benchmark datasets demonstrate that PAGE significantly outperforms state-of-the-art methods, demonstrating its effectiveness for graph anomaly detection.
Many real-world systems can be modeled as graphs, where nodes store and consume entities, actively produce them, or have them emerge naturally, and edges transport them between nodes. This paper studies the networked control problem on such large-scale systems, aiming to decide production and transportation over time to maximize long-term profits, subject to node or edge capacity constraints. Existing SOTAs either fail to guarantee feasibility or cannot scale to large-scale systems. We propose a two-stage policy that integrates a constrained optimization layer after a neural network to explicitly enforce constraints and ensure feasibility. By leveraging the problem structure to obtain expert actions and designing a decision-focused and differentiable loss to enable imitation learning, our method significantly improves efficiency and scalability. In small-scale systems with action dimensions in the order of 10, our method achieves 60x sample efficiency over SOTAs on average. In large-scale systems with action dimensions ranging from 100 to 100000, where SOTAs fail to train, our method converges quickly and outperforms non-learning-based baselines significantly.
In the absence of node attributes, Graph Neural Networks (GNNs) often fail to distinguish locally isomorphic nodes, leading to suboptimal performance. To compensate for this, Positional Information (PI) augmentation has emerged as a powerful technique, which generates attributes by selecting representative nodes as anchors and encoding node-to-anchor distances to other nodes. However, the performance of PI-based methods hinges on two graph-dependent choices: 1) the structural measures used for anchor selection and distance metrics, and 2) the anchor-count K. To obviate manual selections, we propose SCOUT, a model-agnostic augmentation framework that learns a graph-level selector to identify the optimal structural measure and adaptively determines the anchor-count K tailored to each graph and task. Subsequently, leveraging the heavy-tailed distribution typically observed in node centrality, SCOUT utilizes an elbow detection method on the ranked centrality curve to adaptively determine the K most representative nodes as anchors. SCOUT is model-agnostic and enhances various GNNs across downstream tasks. It achieves an improvement of 26.88% in Hits@20 for link prediction on ogbl-ddi and 4.52% accuracy points for node classification on ogbn-arxiv without original attributes; with original attributes, it also brings additional gains of 6.15% AUC on Cora and 11.69% accuracy points on ogbn-arxiv. The source code of SCOUT is available at https://github.com/seinkim01/SCOUT.git.
Federated graph-level clustering (FGC) provides an effective solution for analyzing decentralized graph data with privacy protection. Existing methods typically assume that all clients have the same number of clusters. This assumption simplifies the learning task and has achieved preliminary success. However, this assumption rarely holds in practice, as clients often exhibit substantial heterogeneity in both data distributions and semantic granularity. As a result, cluster-specific knowledge becomes misaligned during server-side aggregation, which ultimately degrades the overall clustering performance. To address this challenge, we propose a novel Federated Graph Clustering under Inter-Client Cluster Number Discrepancy (FedCND) framework, which aligns inter-client heterogeneous distributions by decoupling graph data into public and private patterns. Specifically, after initial local training and clustering on each client, we design a public learner and a private learner to model public and private graph data, respectively. Only anonymized, cluster-level public information is uploaded to the server, while private information remains local. On the server, cluster-level public prototypes are aggregated based on affinities between reconstructed cluster-level graphs, enabling privacy-preserving prototype alignment across clients with heterogeneous cluster numbers and mitigating interference from misaligned information during global aggregation. Finally, private subgraphs derive client-specific prototypes through local relearning, which are subsequently fused with globally oriented public prototypes for better clustering. Extensive experiments demonstrate that the proposed FedCND achieves an average of 4.9% accuracy improvement against current state-of-the-art methods.
For complex networks such as the Web, the Network Dismantling (ND) problem, which asks for the minimum-cost removal of nodes that destroys the giant connected component in the network, is significant in system robustness and misinformation containment. In this paper, we propose a heuristic algorithm, IG+, which is based on reverse dismantling and incorporates novel optimizations. Besides, we design two dynamic algorithms, CCRT-ins and CCRT-rem, employing tree-like indexes to update dismantling results efficiently. Experiments show that our methods outperform state-of-the-art approaches in both effectiveness and efficiency, and can dismantle 10-million-scale networks at arbitrary granularity in a few minutes.
Graph-level anomaly detection (GLAD) is a critical task to identify graphs with abnormal properties in various domains, ranging from fraudulent social networks to malicious botnets on online platforms. The dominant paradigm for existing GLAD detectors has been partially unsupervised, relying on training data composed exclusively of normal samples. However, this partially unsupervised paradigm inevitably requires a costly expert filtering process to ensure the training data is free of anomalies. This creates a significant gap between current approaches and the real-world necessity of a fully unsupervised paradigm, which involves training a model directly on real-world data ''as-is'', with its inherent mix of normal and anomalous samples. To bridge this gap, we incorporate uncertainty learning into GLAD to promote fully unsupervised learning. We propose two frameworks: Score Uncertainty Learning (SUL) and Graph-data Uncertainty Learning (GUL). Specifically, SUL enhances existing GLAD detectors by modeling uncertainty through Gaussian distributions over the detectors' predictions, adaptively attenuating the influence of potential anomalies. GUL is an end-to-end framework that iteratively optimizes anomaly detection and uncertainty modeling via an Expectation-Maximization algorithm. In addition, we develop a dedicated loss that utilizes potential anomalies to enhance the effectiveness and robustness of GUL. Empirical results on sixteen benchmark datasets, covering real-world graphs from social networks and online platforms, demonstrate the superiority of our methods and highlight the promise of incorporating uncertainty into fully unsupervised GLAD.
Every graph hides a tree: through tree decomposition—a foundational tool in modern graph theory with broad applications such as in computational power networks, any network can be unfolded into a hierarchy of overlapping vertex bags whose backbone is a tree. Leveraging this powerful lens, we propose Topological Decomposition for Self-supervised Learning (TopDSL), a framework that injects multi-scale signals into graph representation learning. Concretely, we: 1) decompose the input graph into tree structures with bags representing local structural contexts; 2) compute bag-level roles via closeness centrality for nodes and local edge betweenness for edges, and aggregate these scores across bags to capture context-dependent importance (e.g., local structural bridges); 3) convert the resulting importance and attribute-stability scores into a context-aware augmentation policy that adaptively perturbs nodes, edges, and features—preserving local bridges, honoring multi-community vertices, and attenuating noisy global hubs; 4) construct a new structural similarity loss for contrastive learning, which fuses traditional graph-based proximity with a novel tree-based similarity derived from node co-occurrence in decomposition bags; 5) demonstrate that our framework achieves superior performance over state-of-the-art baselines on various graph learning benchmarks.
Timely detection of anomalous interactions between different entities is crucial for the security and stability of Web-related systems, which are often modeled as streaming graphs. A major issue in existing anomaly detection methods is the effectiveness and the corresponding interpretability. In this paper, we introduce a novel evaluation metric, namely Interaction Willingness, to measure the propensity for entity interactions. Based on this metric, we design two efficient anomaly detection algorithms, AnoD and AnoC, tailored for real-time detection of two prevalent types of anomalous interaction behaviors (dense-type and counter-type), respectively. Notably, we adopt and extend the High-Order Count-Min Sketch for the implicit storage of streaming graphs, and ensure that both the space cost and the time cost of AnoD and AnoC for processing each new streaming edge remain constant and user-controllable, with estimation guarantees. Experimental evaluations on 6 real-world datasets demonstrate that the proposed evaluation metric and the associated algorithms achieve superior detection performance with clear interpretability for detecting anomalous interactions.