Temporal-constraint subgraph matching has emerged as a significant challenge in the study of temporal graphs, which model dynamic relationships across various domains, such as social networks and transaction networks. However, the problem of temporal-constraint subgraph matching is NP-hard. Furthermore, because each temporal-constraint contains a permutation of temporal parameters, existing subgraph matching acceleration techniques demonstrate limited applicability to temporal-constrained graphs. Traditional continuous subgraph matching approaches prove inadequate in addressing this complex problem due to their inability to effectively handle temporal constraints. This paper addresses the challenge of identifying subgraphs that not only structurally align with a given query graph but also satisfy specific temporal-constraints on the edges. We introduce three novel algorithms to tackle this issue: the TCSM-V2V algorithm, which uses a vertex-to-vertex expansion strategy and effectively prunes non-matching vertices by integrating both query and temporal-constraints into a temporal-constraint query graph; the TCSM-E2E algorithm, which employs an edge-to-edge expansion strategy, significantly reducing matching time by minimizing vertex permutation processes; and the TCSM-EVE algorithm, which combines edge-vertex-edge expansion to eliminate duplicate matches by avoiding both vertex and edge permutations. Notably, our optimal TCSM-EVE algorithm achieves an average three-order-of-magnitude speedup on large-scale datasets. Extensive experiments conducted across 6 datasets demonstrate that our approach outperforms existing methods in terms of both accuracy and computational efficiency.

Although directed graphs (digraphs) offer strong modeling capabilities for complex topological systems, existing DiGraph Neural Networks (DiGNNs) struggle to fully capture the concealed rich structural information. This data-level limitation results in model-level sub-optimal predictive performance and underscores the necessity of further exploring the potential correlations between the directed edges (topology) and node profiles (features and labels) from a data-centric perspective, thereby empowering model-centric neural networks with stronger encoding capabilities. In this paper, we propose **E**ntropy-driven **D**igraph knowl**E**dge distillatio**N** (EDEN), which can serve as a data-centric digraph learning paradigm or a model-agnostic hot-and-plug data-centric Knowledge Distillation (KD) module. EDEN implements data-centric machine learning by constructing a coarse-grained Hierarchical Knowledge Tree (HKT) using proposed hierarchical encoding theory, and refining HKT through mutual information analysis of node profiles to guide knowledge distillation during training. As a general framework, EDEN naturally extends to undirected graphs and consistently delivers strong performance. Extensive experiments on 14 (di)graph datasets—spanning both homophily and heterophily settings—and across four downstream tasks show that EDEN achieves SOTA results and significantly enhances existing (Di)GNNs.

Graph Machine Learning is essential for understanding and analyzing relational data. However, privacy-sensitive applications demand the ability to efficiently remove sensitive information from trained graph neural networks (GNNs), avoiding the unnecessary time and space overhead caused by retraining models from scratch.To address this issue, Graph Unlearning (GU) has emerged as a critical solution to support dynamic graph updates while ensuring privacy compliance. Unlike machine unlearning in computer vision or other fields, GU faces unique difficulties due to the non-Euclidean nature of graph data and the recursive message-passing mechanism of GNNs. Additionally, the diversity of downstream tasks and the complexity of unlearning requests further amplify these challenges. Despite the proliferation of diverse GU strategies, the absence of a benchmark providing fair comparisons for GU, and the limited flexibility in combining downstream tasks and unlearning requests, have yielded inconsistencies in evaluations, hindering the development of this domain. To fill this gap, we present OpenGU, the first GU benchmark, where 16 SOTA GU algorithms and 37 multi-domain datasets are integrated, enabling various downstream tasks with 13 GNN backbones when responding to flexible unlearning requests. Through extensive experimentation, we have drawn $10$ crucial conclusions about existing GU methods, while also gaining valuable insights into their limitations, shedding light on potential avenues for future research. Our code is available at \href{https://github.com/bwfan-bit/OpenGU}{https://github.com/bwfan-bit/OpenGU}.

The q-parameterized magnetic Laplacian serves as the foundation of directed graph (digraph) convolution, enabling this kind of digraph neural network (MagDG) to encode node features and structural insights by complex-domain message passing. Despite their success, limitations still exist: (1) The performance of MagDGs depends on selecting an appropriate q-parameter to construct suitable graph propagation equations in the complex domain. This parameter tuning limits model flexibility and significantly increases manual effort. (2) Most approaches treat all nodes with the same complex-domain propagation and aggregation rules, neglecting their unique digraph contexts. This oversight results in sub-optimal performance. To address the above issues, we propose two key techniques: (1) MAP is crafted to be a plug-and-play complex-domain propagation optimization strategy, enabling seamless integration into any MagDG to improve predictions while enjoying high running efficiency. (2) MAP++ is a new digraph learning framework, further incorporating a learnable mechanism to achieve adaptively edge-wise propagation and node-wise aggregation in the complex domain for better performance. Extensive experiments on 12 datasets demonstrate that MAP enjoys flexibility for it can be incorporated with any MagDG, and scalability as it can deal with web-scale digraphs. MAP++ achieves SOTA predictive performance on 4 different downstream tasks.

Truss decomposition is a fundamental approach in graph theory that focuses on uncovering cohesive subgraphs within networks. However, many networks involve groupwise rather than pairwise relationships and are often represented as hypergraphs. Modeling and capturing k-truss in hypergraphs is essential for uncovering tight-knit relationships in such multi-relational networks. In this paper, we tackle the problem of truss decomposition in hypergraph. A hyper k-truss is a subgraph in which each node is part of at least k hyper-triangles. We first introduce a framework for hyper-truss decomposition and determine that the most time-consuming component is counting hyper-triangles. To count all hyper-triangles efficiently, we propose an edge-iterator algorithm. To further reduce redundant computations, we present an improved algorithm that combines edge-iterator and node-iterator techniques to prune non-promising nodes. Next, to handle common nodes in hypergraphs, we develop a novel prefix forest technique to encode all hyperedges and count triangles within this prefix forest. We also propose several optimization strategies that reorder nodes and hyperedges to improve work balancing. Finally, we conduct extensive experiments on real-world hypergraph datasets, demonstrating the efficiency and effectiveness of our algorithms.

Although the widespread use of AI systems in today's world is growing, many current AI systems are found vulnerable due to hidden bias and missing information, especially in the most commonly used forecasting system. In this work, we explore the robustness and explainability of AI-based forecasting systems. We provide an in-depth analysis of the underlying causality involved in the effect prediction task and further establish a causal graph based on treatment, adjustment variable, confounder, and outcome. Correspondingly, we design a causal interventional prediction system (CIPS) based on a variational autoencoder and fully conditional specification of multiple imputations. Extensive results demonstrate the superiority of our system over state-of-the-art methods and show remarkable versatility and extensibility in practice.

Marketing campaigns are a set of strategic activities that can promote a business's goal. The effect prediction for marketing campaigns in a real industrial scenario is very complex and challenging due to the fact that prior knowledge is often learned from observation data, without any intervention for the marketing campaign. Furthermore, each subject is always under the interference of several marketing campaigns simultaneously. Therefore, we cannot easily parse and evaluate the effect of a single marketing campaign. To the best of our knowledge, there are currently no effective methodologies to solve such a problem, i.e., modeling an individual-level prediction task based on a hierarchical structure with multiple intertwined events. In this paper, we provide an in-depth analysis of the underlying parse tree-like structure involved in the effect prediction task and we further establish a Hierarchical Capsule Prediction Network (HapNet) for predicting the effects of marketing campaigns. Extensive results based on both the synthetic data and real data demonstrate the superiority of our model over the state-of-the-art methods and show remarkable practicability in real industrial applications.