With the explosive adoption of web-based technology, the amount of graph-structured data has increased dramatically, resulting in a higher demand to find anomalous patterns in different types of online services, such as fraudulent transactions, fake accounts, and coordinated malicious campaigns. The performance of anomaly detection in graphs of web systems is a challenge due to the sparse and camouflaged nature of such anomalies, multi-granular irregularity features, and the instability of the generative models in a real-world web application. To address these constraints, we introduce a new unified generative framework GRAND (Graph Anomaly Detection via Diffusion) suitable for graph data of the web domain. GRAND applies a novel dual-diffusion strategy: continuous Gaussian diffusion for node features and discrete diffusion for edges, combined with a structural-prior-conditioned graph transformer denoiser. Besides this, the framework adds strong anomaly scoring mechanisms with adaptive pooling and normalization schemes to detect the subtle anomaly signals typical of web data. It provides degeneracy detection for inference stability. GRAND has been demonstrated to obtain better results than state-of-the-art methods by extensive evaluations of different benchmark datasets. GRAND demonstrates strong performance in the detection of money laundering, particularly on the Elliptic dataset, a Bitcoin transaction graph typically for financial web applications. © 2026 Owner/Author.

The message-passing paradigm of Graph Neural Networks often struggles with exchanging information across distant nodes typically due to structural bottlenecks in certain graph regions, a limitation known as over-squashing. To reduce such bottlenecks, graph rewiring, which modifies graph topology, has been widely used. However, existing graph rewiring techniques often overlook the need to preserve critical properties of the original graph, e.g., spectral properties. Moreover, many approaches rely on increasing edge count to improve connectivity, which introduces significant computational overhead and exacerbates the risk of over-smoothing. In this paper, we propose a novel graph-rewiring method that leverages spectral graph sparsification for mitigating over-squashing. Specifically, our method generates graphs with enhanced connectivity while maintaining sparsity and largely preserving the original graph spectrum, effectively balancing structural bottleneck reduction and graph property preservation. Experimental results validate the effectiveness of our approach, demonstrating its superiority over strong baseline methods in classification accuracy and retention of the Laplacian spectrum.

Graph Neural Networks (GNNs) have gained significant attention as a powerful modeling and inference method, especially for homophilic graph-structured data. To empower GNNs in heterophilic graphs, where adjacent nodes exhibit dissimilar labels or features, Signed Message Passing (SMP) has been widely adopted. However, there is a lack of theoretical and empirical analysis regarding the limitations of SMP. In this work, we unveil the potential pitfalls of SMP and their remedies. We first identify two limitations of SMP: undesirable representation update for multi-hop neighbors and vulnerability against oversmoothing issues. To overcome these challenges, we propose a novel message-passing function called Multiset to Multiset GNN (M2M-GNN). Our theoretical analyses and extensive experiments demonstrate that M2M-GNN effectively alleviates the limitations of SMP, yielding superior performance in comparison.

Graph Neural Networks (GNNs) have attracted much attention due to their superior learning capability. Despite the successful applications of GNNs in many areas, their performance suffers heavily from the long-tailed node degree distribution. Most prior studies tackle this issue by devising sophisticated model architectures. In this article, we aim to improve the performance of tail nodes (low-degree or hard-to-classify nodes) via a generic and light normalization method. In detail, we propose a novel normalization method for GNNs, termed as ResNorm, whichReshapes a long-tailed distribution into a normal-like distribution viaNormalization. The ResNorm includes two operators. First, thescaleoperator reshapes the distribution of the node-wise standard deviation (NStd) so as to improve the accuracy of tail nodes. Second, the analysis of the behavior of the standard shift indicates that the standard shift serves as a preconditioner on the weight matrix, increasing the risk of over-smoothing. To address this issue, we design a newshiftoperator for ResNorm, which simulates the degree-specific parameter strategy in a low-cost manner. Extensive experiments on various node classification benchmark datasets have validated the effectiveness of ResNorm in improving the performance of tail nodes as well as the overall performance.

Graph Neural Networks (GNNs) have been shown to achieve remarkable performance on node classification tasks by exploiting both graph structures and node features. The majority of existing GNNs rely on the implicit homophily assumption. Recent studies have demonstrated that GNNs may struggle to model heterophilous graphs where nodes with different labels are more likely connected. To address this issue, we propose a generic GNN applicable to both homophilous and heterophilous graphs, namely Low-Rank Graph Neural Network (LRGNN). Our analysis demonstrates that a signed graph's global label relationship matrix has a low rank. This insight inspires us to predict the label relationship matrix by solving a robust low-rank matrix approximation problem, as prior research has proven that low-rank approximation could achieve perfect recovery under certain conditions. The experimental results reveal that the solution bears a strong resemblance to the label relationship matrix, presenting two advantages for graph modeling: a block diagonal structure and varying distributions of within-class and between-class entries.