Data-driven spectrum sensing is a key technology for addressing complex challenges in Cognitive Radio Networks (CRNs). Traditional methods are typically designed for simple single-band scenarios and perform poorly in practical wideband applications. In real-world systems, a single Secondary User (SU) is often restricted by energy, time, and hardware capabilities during real-time sensing. Consequently, only local and fragmented frequency information can be obtained. This partial sensing leads to a severe lack of training data. Additionally, the lack of historical records for emerging frequency bands, combined with data incompleteness due to resource constraints, creates training bottlenecks for data-driven models and limits the reliability of sensing. To address these challenges, this paper proposes a novel framework based on Collaborative Subgraph Learning and Hyperbolic Graph Neural Networks (GNNs). This approach enables Secondary Users to perform collaborative sensing through distributed subgraph learning. By utilizing GNNs to extract features and model multi-band correlations, a new distributed GNNs architecture is designed to efficiently detect wideband spectrum occupancy, even with partial observations. Within this framework, all frequency bands in the wideband spectrum pool are treated as a unified graph, while the bands observed by each SU form a subgraph. Subsequently, the complete spectrum graph is constructed through the joint training and aggregation of these subgraphs. By integrating hyperbolic geometry into GNNs, this method better captures the hierarchical structure of spectrum patterns, providing a more accurate and efficient sensing model. Experimental results demonstrate that, compared to the second-best HCNNs model, the proposed framework improves sensing accuracy by 3.8% on average across various test environments, while reducing key resource consumption by 18.4% on average.
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Detecting data that deviates from normal behavior in dynamic graphs is an important hotspot. In the real world, anomaly detection is widely applied across various domains. However, existing anomaly detection methods typically assume static input graphs, failing to capture dynamic information in real-world scenarios. In addition, during the evolution of node representations over time, standard updating mechanisms lack the ability to selectively preserve important features. To address these issues, this paper constructs a dynamic graph anomaly detection framework (DyConAD) that enhances model perception of dynamic information through memory enhancement strategies and multi-scale similarity-based anomaly scoring mechanisms. Additionally, we also design a dynamic graph construction method that extracts time-aware shapelet and establishes spatiotemporal relationships between these shapelet. Experimental validation is conducted on four real-world datasets and three public datasets from the UCR Time Series Archive. Results demonstrate that our proposed method outperforms existing approaches across multiple datasets, achieving effective improvements in both detection accuracy and efficiency.
Graph contrastive learning has emerged as a promising self-supervised approach for node representation learning, reducing reliance on human annotations. However, its limitation for modeling high-order structures leads to: loss of critical edges and nodes, diminished discriminability for higher-order semantics, and indistinguishable negative samples. To address these limitations, we propose SPGCL, a Subgraph Pattern-Aware Graph Contrastive Learning for Structural Representation. SPGCL enables the model to capture high-order structures by leveraging subgraph patterns. Specifically, SPGCL introduces subgraph patterns to differentiate high-order structures and preserve edges crucial for distinguishing these structures. In addition, it internalizes the subgraph pattern features into SP edge features, SP node features, and SP adjacency matrices to provide a more comprehensive structural representation. Furthermore, it utilizes subgraph pattern similarity and distance similarity, and restructures graph contrastive loss to sharpen negative-sample discrimination. Experiments on six real-world datasets demonstrate that SPGCL significantly outperforms state-of-the-art baselines.
Graph-level classification involves analyzing the property of the whole graph, which is typically solved by using graph neural networks (GNNs). Existing efforts generally assume a balanced class distribution. However, real-world data often exhibit long-tailed distributions, i.e., tail classes have significantly fewer samples than head classes, and thus directly applying GNNs is eventually biased toward the head classes, resulting in limited generalization over the tail classes. Moreover, the predictions of existing algorithms are usually not trustworthy, and the trained classifiers remain ignorant to their predictive confidence. Towards this end, in this paper we develop a principled framework called GraphEVER for long-tailed graph-level classification. Technically, GraphEVER incorporates the beliefs of multiple experts and leverages the idea of subjective logic within the Dempster-Shafer Evidence Theory (DST). It can provide the evidence and uncertainty estimation for each expert, where the evidence is parameterized by a Dirichlet distribution to model class probability distribution, and the uncertainty is quantified via a well-defined theoretical framework. In this way, diverse experts can be integrated under DST to endow the classifier with both reliability and robustness. Moreover, we propose an evidence-based routing mechanism to dynamically assign experts, such that the tail classes can receive more attention, while the head classes can reduce redundant engaged experts, further cutting down the computational cost and improving the efficiency. Extensive experiments on seven datasets verify the superiority of our proposed framework.
Many real-world datasets, such as citation networks, social networks, and molecular structures, are naturally represented as heterogeneous graphs, where nodes belong to different types and have additional features. For example, in a citation network, nodes representing ''Paper'' or ''Author'' may include attributes like keywords or affiliations. A critical machine learning task on these graphs is node classification, which is useful for applications such as fake news detection, corporate risk assessment, and molecular property prediction. Although Heterogeneous Graph Neural Networks (HGNNs) perform well in these contexts, their predictions remain opaque. Existing post-hoc explanation methods lack support for actual node features beyond one-hot encoding of node type and often fail to generate realistic, faithful explanations. To address these gaps, we propose DiGNNExplainer, a model-level explanation approach that synthesizes heterogeneous graphs with realistic node features via discrete denoising diffusion. In particular, we generate realistic discrete features (e.g., bag-of-words features) using diffusion models within a discrete space, whereas previous approaches are limited to continuous spaces. We evaluate our approach on multiple datasets and show that DiGNNExplainer produces explanations that are realistic and faithful to the model's decision-making, outperforming state-of-the-art methods.
Explaining the decision-making process of Graph Neural Networks (GNNs) is essential for improving their transparency and reliability. However, real-world graphs are often heterogeneous and subject to structural noise, posing severe challenges to the robustness of existing explanation methods. To address these issues, we propose RoHeX, a Robust Heterogeneous GNN Explainer that enhances explanation quality under noisy conditions. RoHeX begins with a theoretical analysis revealing how different heterogeneous GNN architectures amplify structural perturbations through message passing. Building on this insight, we design a denoising variational inference framework that filters noisy structures and learns robust latent graph representations. Furthermore, we incorporate relation-aware heterogeneous semantics into the explanation generation process, formulating explanation as an optimization problem under the graph information bottleneck principle. This formulation enables RoHeX to balance fidelity and compactness, producing explanations that are both semantically meaningful and structurally stable. Comprehensive experiments on multiple real-world heterogeneous graphs demonstrate that RoHeX consistently surpasses state-of-the-art baselines in explanation fidelity, robustness to structural perturbations, and explainability.
Graph Masked Autoencoders (GMAEs) have emerged as a notable self-supervised learning approach for graph-structured data. Existing GMAE models primarily focus on reconstructing node-level information, categorizing them as single-scale GMAEs. This methodology, while effective in certain contexts, tends to overlook the complex hierarchical structures inherent in many real-world graphs. For instance, molecular graphs exhibit a clear hierarchical organization in the form of the atoms-functional groups-molecules structure. Therefore, the inability of single-scale GMAE models to incorporate these hierarchical relationships often results in an inadequate capture of crucial high-level graph information, leading to a noticeable decline in performance. To address this limitation, we propose Hierarchical Graph Masked AutoEncoders (Hi-GMAE), a novel multi-scale GMAE framework designed to handle the hierarchical structures within graphs. First, Hi-GMAE constructs a multi-scale graph hierarchy through graph pooling, enabling the exploration of graph structures across different granularity levels. To ensure masking uniformity of subgraphs across these scales, we propose a novel coarse-to-fine strategy that initiates masking at the coarsest scale and progressively back-projects the mask to finer scales. Furthermore, we integrate a gradual recovery strategy with the masking process to mitigate the learning challenges posed by completely masked subgraphs. Diverging from the standard graph neural network (GNN) used in GMAE models, Hi-GMAE modifies its encoder and decoder into hierarchical structures. This entails using GNN at the finer scales for detailed local graph analysis and employing a graph transformer at coarser scales to capture global information. Such a design enables Hi-GMAE to effectively capture the multi-level information inherent in complex graph structures. Our experiments on 17 graph datasets, covering two graph learning tasks, consistently demonstrate that Hi-GMAE outperforms 29 state-of-the-art self-supervised competitors in capturing comprehensive graph information.
Contrastive learning has strong generalization ability and the capability to learn automatically without labeled information. However, it still faces challenges such as insufficient feature diversity, a lack of multi-level semantics, and the balance between tolerance and consistency. To address these challenges, This study propose a Multi-view Hierarchical Graph Contrastive Learning method. First, a new view is generated through a diffusion matrix to provide multi-view data for contrastive learning. Then, these multi-view data are fed into an asynchronous asymmetric network structure, specifically using graph network models to learn diversified features. Next, we adopt a self-designed hierarchical contrastive learning framework, constructing a three-level contrastive loss for joint optimization of nodes, subgraphs, and global graphs. Meanwhile, we introduce alignment and consistency and appropriately adjust the loss function through a temperature coefficient. Ultimately, the model achieves excellent classification performance on multiple datasets through node classification and graph classification tasks.
Graph Neural Networks (GNNs) are vulnerable to graph backdoor attacks, which poses severe risks to their deployment in safety-critical applications. Existing defenses predominantly focus on specific backdoor triggers, making them brittle and unable to generalize across different backdoor triggers with varying properties. Motivated by this limitation, this work proposes an attack-agnostic graph backdoor defense mechanism A2GBD, which does not require prior knowledge of the specific attack strategies (e.g., edge perturbation, node attribute manipulation) to achieve effective defense. A2GBD consists of suspicious node selection and defense strategy generation. The selection module selects high-suspicion nodes to enhance defense awareness, while the defense agent adaptively determines and executes defense strategies. Extensive experiments on multiple benchmark datasets demonstrate that A2GBD consistently lowers attack success rates while maintaining high clean accuracy, showing strong robustness and generalizability against diverse graph backdoor attack strategies.
Text-attributed graphs (TAGs) enhance graph learning by integrating rich textual semantics and topological context for each node. While boosting expressiveness, they also expose new vulnerabilities in graph learning through text-based adversarial surfaces. Recent advances leverage diverse backbones, such as graph neural networks (GNNs) and pre-trained language models (PLMs), to capture both structural and textual information in TAGs. This diversity raises a key question: How can we design universal adversarial attacks that generalize across architectures to assess the security of TAG models? The challenge arises from the stark contrast in how different backbones—GNNs and PLMs—perceive and encode graph patterns, coupled with the fact that many PLMs are only accessible via APIs, limiting attacks to black-box settings. To address this, we propose BadGraph, a novel attack framework that deeply elicits large language models' (LLMs) understanding of general graph knowledge to jointly perturb both node topology and textual semantics. Specifically, we design a target influencer retrieval module that leverages graph priors to construct cross-modally aligned attack shortcuts, thereby enabling efficient LLM-based perturbation reasoning. Experiments show that BadGraph achieves universal and effective attacks across GNN- and LLM-based reasoners, with up to a 76.3% performance drop, while theoretical and empirical analyses confirm its stealthy yet interpretable nature.
Graph self-supervised learning (GSSL) alleviates the graph data labeling bottleneck without supervision, enabling wide application in domains like recommendation systems and social network analysis. High-frequency signals are valuable in GSSL for capturing local structural preferences, thereby enriching graph representations and boosting model performance. However, in practical applications, two critical problems hinder the efficient and robust use of these signals. First, the locality of high-frequency signals limits their full utilization by the model. Second, over-reliance on specific high-frequency signals will affect the model's generalization. To address the above problems, we propose the Frequency-Corrupt Based Graph Self-Supervised Learning (FC-GSSL) algorithm. Specifically, we generate corrupted graphs biased toward high-frequency signals by corrupting nodes and edges according to their low-frequency contributions. These corrupted graphs are fed as input to an autoencoder, with low-frequency and general features serving as the supervision. This compels the model to effectively fuse high- and low-frequency signals, thereby integrating and utilizing more valuable high-frequency information. Additionally, we design multiple sampling strategies and form diverse corrupted graphs based on the intersections and union between the results obtained from these strategies. By aligning the node representations from these views, the model can identify valuable frequency combinations, which helps reduce the negative impact of specific high-frequency components and improve generalization. FC-GSSL optimizes the design of GSSL for web applications, significantly improving model performance on complex web-related graphs, such as social networks and citation networks. This work makes a direct contribution to advancing the ''Graph Algorithms and Modeling for the Web'' research track. Experimental results on 14 datasets across multiple tasks illustrate the superiority of the proposed approach.
Graph generation is a fundamental problem in graph learning with broad applications across Web-scale systems, knowledge graphs, and scientific domains such as drug and material discovery. Recent approaches leverage diffusion models for step-by-step generation, yet unconditional diffusion offers little control over desired properties, often leading to unstable quality and difficulty in incorporating new objectives. Inference-time guidance methods mitigate these issues by adjusting the sampling process without retraining, but they remain inherently local, heuristic, and limited in controllability. To overcome these limitations, we propose TreeDiff, a Monte Carlo Tree Search (MCTS) guided dual-space diffusion framework for controllable graph generation. TreeDiff is a plug-and-play inference-time method that expands the search space while keeping computation tractable. Specifically, TreeDiff introduces three key designs to make it practical and scalable: (1) a macro-step expansion strategy that groups multiple denoising updates into a single transition, reducing tree depth and enabling long-horizon exploration; (2) a dual-space denoising mechanism that couples efficient latent-space denoising with lightweight discrete correction in graph space, ensuring both scalability and structural fidelity; and (3) a dual-space verifier that predicts long-term rewards from partially denoised graphs, enabling early value estimation and removing the need for full rollouts. Extensive experiments on 2D and 3D molecular generation benchmarks, under both unconditional and conditional settings, demonstrate that TreeDiff achieves state-of-the-art performance. Notably, TreeDiff exhibits favorable inference-time scaling: it continues to improve with additional computation, while existing inference-time methods plateau early under limited resources.
Graph anomaly detection identifies abnormal patterns in networks but faces label scarcity and extreme class imbalance. While graph contrastive learning offers unsupervised solutions, existing methods suffer from two limitations: random augmentations break semantic consistency in positive pairs, while naive negative sampling produces trivial contrasts. We propose AC2L-GAD, an Active Counterfactual Contrastive Learning framework addressing both limitations through principled counterfactual reasoning. By combining information-theoretic active selection with counterfactual generation, our approach identifies structurally complex nodes and generates anomaly-preserving positive augmentations alongside hard negative contrasts, while restricting expensive counterfactual generation to a strategically selected subset. This design reduces computational overhead by approximately 65% compared to full-graph counterfactual generation while maintaining detection quality. Experiments on nine benchmark datasets, including real-world financial transaction graphs from GADBench, show that AC2L-GAD achieves competitive or superior performance compared to state-of-the-art baselines, with notable gains in datasets where anomalies exhibit complex attribute-structure interactions.
Identification of Influential Node Group in Attributed Graph through Explaining Graph Neural Network
Identification of influential groups of nodes in attributed graphs has applications in a wide range of real-world problems, for instance, collecting important proceedings in citation networks, or identifying essential genes for diagnosing disease in Protein-Protein Interaction networks. Previous approaches for influence maximization manipulated on the graph structure, despite their proliferation, neglect the node attribute information containing additional knowledge. In this work, we introduce Global Graph UNderstanding (GGUN), a perturbation-based framework leveraging the explanatory power of Graph Neural Networks. It takes into account the entire graph structure and node attributes simultaneously and fuses knowledge through GNN layers. Following the perturbation-based explanation, GGUN fills the gap between Deep Neural Network gradient-based feature importance analysis and discrete structure in the graph, which is formulated as a combinatorial optimization problem. Moreover, GGUN obtains an efficient solution by relaxing the infeasible combinatorial optimization problem with performance guaranteed. Evaluations of synthetic and real-world datasets show that GGUN outperforms baselines on both quantitative metrics and human-intelligible analysis.
Out-of-Distribution (OOD) detection, which seeks to identify samples deviating from the In-Distribution (ID) training distribution at test time, is crucial for building robust machine learning systems. While extensive efforts have been made for Euclidean data, OOD detection on graph-structured data remains relatively underexplored. On the one hand, the specific properties of a graph may be attributed to its substructures. On the other hand, acquiring labeled data for graph learning is typically time-consuming and labor-intensive. Toward this end, in this paper, we propose a novel kernel-enhanced graph substructure learning framework termed KEGOD for unsupervised graph OOD detection. Specifically, we introduce a learnable graph generator to construct the augmented graph view that preserves distinguishable structure information. Then, for both the input graph and augmented view, a graph neural network (GNN) branch and a graph kernel (GK) branch are incorporated to explore graph latent patterns. By performing multi-branch concordance learning on the extracted graph patterns, our KEGOD captures complementary ID structural semantics in both implicit and explicit manners, enabling reliable detection of OOD graphs through semantic inconsistency. Finally, we build a self-adaptive training mechanism to automatically control diverse sensitivities of the graph patterns. Experimental results on several public graph datasets reveal the superiority of our KEGOD. Our code is available at~ https://github.com/jamesyifan/KEGOD.
Molecule graph editing has become a powerful paradigm for optimizing chemical compounds in drug discovery. Existing methods overlook the invariant structure-property relationships, and rely on variable correlations that shift across different instructions, thereby failing to generalize to out-of-distribution (O.O.D.) scenarios. To overcome the weakness of existing work, in this paper we propose to capture and utilize the invariant factors in order to achieve generalizable molecule graph editing under distribution shifts. However, this problem remains challenging, given that the invariant and variant factors are deeply entangled within the editing models. To tackle this challenge, we propose MoFE, a disentangled graph large language model for molecule graph editing that handles editing instructions under distribution shifts via disentangling invariant factors that govern editing-relevant properties. Specifically, we propose a disentangled graph projector with invariance loss that encodes molecular graphs into disentangled latent factors, with an invariance loss that ensures consistency across paraphrased prompts with the same objective. Then, we enhance the LLM with a factor-aware LoRA mixture-of-experts, where each expert is associated with a distinct latent factor. Additionally, we introduce a factor disentanglement loss weighting strategy that adaptively assigns higher weights to expert-factor pairs that perform well on relevant editing tasks. The proposed MoFE model promotes joint disentanglement between experts and latent factors, reinforcing their alignment and preventing collapse. Experiments on a representative benchmark demonstrate that MoFE is able to achieve superior O.O.D. generalization performance in molecule graph editing.
Heterophily in graphs is a key challenge for Graph Neural Networks (GNNs). By proposing various homophily measures, recent work has provided insights into how heterophily affects node classification. However, while both graph homophily and heterophily can be further refined into diverse connection patterns, previous work has largely overlooked the role of connection pattern inconsistency. In this paper, we delve deeper into heterophily and homophily by shifting from coarse-grained heterophily ratios to a unified, fine-grained formulation based on connection patterns, and we further reveal an uneven distribution and a train–test gap of these patterns. Empirical studies indicate that this inconsistency leads to severe performance disparity. To address this issue, we propose a novel two-stage method named IVQ-GNN. In the pre-training phase, IVQ-GNN encodes diverse connection patterns into a codebook that serves as an orthogonal basis for the representation space. In the fine-tuning phase, a self-attention module linearly combines these orthogonal bases to expand the learned token space of connection patterns, thereby improving adaptation to rare and out-of-distribution (OOD) patterns. Experimental results on multiple datasets demonstrate that IVQ-GNN significantly improves model performance and validate that the proposed method effectively addresses the connection pattern inconsistency. Our code is available at https://github.com/Duyx5149/IVQ-GNN.
Graph anomaly detection (GAD) aims to identify nodes that deviate from normal patterns in structure or features. While recent GNN-based approaches have advanced this task, they struggle with two major challenges: 1) homophily disparity, where nodes exhibit varying homophily at both class and node levels; and 2) limited scalability, as many methods rely on costly whole-graph operations. To address them, we propose SAGAD, a Scalable and Adaptive framework for GAD. SAGAD precomputes multi-hop embeddings and applies reparameterized Chebyshev filters to extract low- and high-frequency information, enabling efficient training and capturing both homophilic and heterophilic patterns. To mitigate node-level homophily disparity, we introduce an Anomaly Context-Aware Adaptive Fusion, which adaptively fuses low- and high-pass embeddings using fusion coefficients conditioned on Rayleigh Quotient-guided anomalous subgraph structures for each node. To alleviate class-level disparity, we design a Frequency Preference Guidance Loss, which encourages anomalies to preserve more high-frequency information than normal nodes. SAGAD supports mini-batch training, achieves linear time and space complexity, and drastically reduces memory usage on large-scale graphs. Theoretically, SAGAD ensures asymptotic linear separability between normal and abnormal nodes under mild conditions. Extensive experiments on 10 benchmarks confirm SAGAD's superior accuracy and scalability over state-of-the-art methods.
Graph Transformer has demonstrated impressive capabilities in the field of graph representation learning. However, existing approaches face two critical challenges: (1) most models suffer from exponentially increasing computational complexity, making it difficult to scale to large graphs; (2) attention mechanisms based on node-level operations limit the flexibility of the model and result in poor generalization performance in out-of-distribution (OOD) scenarios. To address these issues, we propose VecFormer (the Vec tor Quantized Graph Transformer ), an efficient and highly generalizable model for node classification, particularly under OOD settings. VecFormer adopts a two-stage training paradigm. In the first stage, two codebooks are used to reconstruct the node features and the graph structure, aiming to learn the rich semantic Graph Codes. In the second stage, attention mechanisms are performed at the Graph Token level based on the transformed cross codebook, reducing computational complexity while enhancing the model's generalization capability. Extensive experiments on datasets of various sizes demonstrate that VecFormer outperforms the existing Graph Transformer in both performance and speed.
Cross-domain recommendation (CDR) has emerged as a promising solution by effectively alleviating data sparsity by leveraging information from auxiliary domains. However, a major challenge in CDR is its dependence on predefined alignment rules (e.g., structural or distribution matching) to achieve cross-domain knowledge transfer, which impose fixed transfer patterns and lack the flexibly need for diverse cross-domain scenarios. Furthermore, most existing approaches still rely on coarse-grained representations. Knowledge transfer built upon imprecise representations can, even with improved alignment rules, instead lead to negative transfer in the target domain. To address these challenges and optimize recommendation efficacy, a new framework named meta-learning driven few-shot knowledge transfer with dual-stage adaptive data replay for cross-domain recommendation (MFACDR) is proposed. Specifically, a new meta-learning driven few-shot knowledge transfer method is proposed. This method leverages overlapping parts as anchors to guide the non-overlapping parts in autonomously exploring alignment rules through meta-learning, thus enabling few-shot knowledge transfer and flexible handling of different cross-domain scenarios. In addition, a dual-stage adaptive data replay mechanism is proposed, which enables fine-grained cross-domain adaptability and helps to mitigate negative transfer. Extensive experiments on three real-world datasets consistently demonstrate the superior effectiveness and robustness of the proposed MFACDR.