Graph-structured data effectively captures complex relationships in diverse domains such as social networks, financial transactions, citation networks, and recommendation systems. Graph Neural Networks (GNNs) excel in learning intricate topological patterns, yielding strong performance on tasks like node classification and link prediction. However, real-world graphs often scale to millions of nodes and billions of directed edges, posing significant computational and storage challenges for GNN training that frequently exceed available hardware limits. Although graph sampling and distillation techniques alleviate these issues by subsampling or creating surrogate graphs, they primarily handle undirected graphs, neglecting directional semantics that are crucial for applications like fraud detection and causal analysis. To address these limitations, we introduce the Directed Graph Distillation (Dir-GD) framework, which combines distributed learning with community detection to divide large directed graphs into independent subgraphs for distributed directed GNN training. This process culminates in parameter aggregation to produce a compact global synthetic graph that preserves essential topology and directionality. Extensive experiments on large-scale datasets, such as the million-node soc-pokec-relationships, demonstrate over 91% accuracy at 0.001 distillation ratios, accompanied by substantial memory and runtime savings. This work pioneers directed graph distillation as a key paradigm for analyzing ultra-large directed graphs, offering a scalable solution that maintains high fidelity in compressed representations.

Recent studies have shown that Heterogeneous Graph Neural Networks (HetGNNs) are vulnerable to adversarial attacks. Existing methods rely on the gradient information of source models or surrogate models to generate perturbations, which limits the attack of transferability and effectiveness in real-world attack scenarios, while consuming time costs. In this paper, we propose a novel framework, i.e., Transferable Black-Box Injection Attack against Heterogeneous Graph Neural Networks (TBI-Attack), to address these challenges. Specifically, we introduce a voting-based key nodes recognizer based on different meta-paths to identify key nodes in relational subgraphs. Subsequently, we present a semantic-confused feature generator that leverages self-supervised learning to integrate neighborhood information from different relational subgraphs, generating malicious nodes with conflicting semantic features. Furthermore, malicious nodes are injected into various relational subgraphs, disrupting their specific semantic functionality and systematically impairing the message-passing process of HetGNNs. Extensive experiments are conducted on four authentic datasets to validate the effectiveness and transferability of TBI-Attack and the corresponding superiority to state-of-the-art methods.

In the realm of real-world knowledge graphs, the dynamism of facts is a prevailing characteristic. To illustrate, a popular restaurant was awarded a Michelin star in 2004 and retained this prestigious recognition in 2008, but lost it in 2012 due to changes in management and menu quality. This sequence highlights how neglecting temporal context can lead to misconceptions about factual accuracy. Furthermore, the relations intertwining distinct entities or the same entity across different chronological markers exhibit complexity and hierarchy. Regrettably, existing methods for temporal knowledge graph relation prediction fall short in following challenges: they lack a nuanced, hierarchical comprehension of knowledge structure and fail to adeptly integrate temporal dynamics with static attributes. Addressing these issues, this study introduces Hyperbolic-based Temporal Knowledge Graph Relation Prediction (HTKGP) approach to harness the power of hyperbolic geometry. Our innovation is an attention-guided, learnable curvature mechanism designed to preserve and enrich the intricate semantic hierarchy inherent in data. Besides, we propose a longitudinal information entity embedding strategy due to the plentiful temporal information. This not only captures the enduring impact of past events on present states but also achieves efficiency through parameter reduction. Empirical validation across multiple datasets shows HTKGP efficiently navigates the rich semantic landscape within hyperbolic spaces and yields superior predictive performance. Our implementations are publicly available at: https://github.com/jianruichen/HTKGP .

Knowledge tracing aims to dynamically track and assess learners’ mastery of specific knowledge concepts (e.g., item taxonomies, skill hierarchies). Integrating it into recommender systems greatly enhances model explainability, yet current models either overemphasize temporal dynamics or overlook inter-concept spatial correlations, resulting in suboptimal performance in integrated spatiotemporal modeling. Such disjointed designs also lead to limited adaptability in long learning sequences, poor compatibility with real-world dynamic scenarios, and restricted model interpretability. To solve these problems, we propose an A-SGNN framework fusing higher-order path spiking and graph neural networks, which leverages Graph Convolutional Network (GCN) and Spiking Neural Network (SNN) modules to make up for existing shortcomings. Specifically, a Bidirectional GCN module fully captures bidirectional high-order spatial graph structures between concepts, accurately modeling multi-knowledge relationships and reducing information loss. An SNN module with adaptive path-finding strategy dynamically optimizes individual learning trajectories, overcoming traditional fixed-path rigidity, while its membrane potential decay simulates human forgetting. A time decay factor is integrated to better capture memory effects in learning. Experiments demonstrate that our method outperforms state-of-the-art approaches in predicting learners’ future academic performance, with this advantage deriving from the combined synergistic benefits of the GCN and SNN modules. Our implementation is publicly available at: https://github.com/jianruichen/A-SGNN .

Disease-related association prediction is a crucial task in the biomedical field, aiming to identify relations between diseases and various biological entities such as RNAs (like circRNAs, lncRNAs), drugs and genes. Understanding these interactions not only deepens our understanding of pathological mechanisms, but also facilitates the development of novel diagnostic tools, therapeutic strategies, and preventive measures. Current challenges in disease-related association prediction primarily encompass data sparsity, data heterogeneity, limited generalization ability, and the absence of a unified analytical framework. To address the above issues, we propose a hybrid framework integrating dynamics mechanisms and graph convolutional networks in hyperbolic space for disease-related association prediction. Our approach begins by constructing a heterogeneous network using interaction information to represent multiple types of biological associations. This network is then processed through a game-guided dynamics mechanism that incorporates both individual node features and other influences. The hyperbolic graph convolutional network is then designed to model hierarchical and scale-free graph-structured data. Comprehensive experimental results on multiple types of associations demonstrate that our model achieves high predictive performance. The results of the case study validate the robust predictive capability of our proposed method in the prediction of disease-related associations.

Since severe environmental problem in manufacturing industries is becoming increasingly prominent, energy-efficient production scheduling has gained more and more attentions. This paper studies an energy-efficient distributed fuzzy hybrid blocking flow-shop scheduling problem (EEDFHBFSP), where processing time and setup time are uncertain. The objective is to minimize fuzzy makespan and total fuzzy energy consumption simultaneously. To solve such problem, a mixed-integer linear programming model is firstly presented to format it. Then, a meta-Q-learning-based multi-objective metaheuristic (MQL-MM) is proposed. In MQL-MM, a machine-position-based dispatch rule is designed as the decoding scheme. A decomposition-based constructive heuristic is employed to generate the initial population with high quality and diversity. Several problem-specific search operators are developed to explore and exploit the solution space. A meta-Q-learning-based multi-objective search framework is presented to guide the using of search operators, which includes a meta-training phase and an adaptive search phase. The meta-training phase is employed to train the search operators to construct the Q-learning model. The adaptation search phase utilizes such model to conduct the automatic selection of the search operators. Moreover, an energy saving strategy is designed to improve the candidate solutions. Finally, we conduct extensive experiments. The experimental results show that the designs of MQL-MM are effective, and MQL-MM performs better than several well-performing methods on solving EEDFHBFSP.

Drug-Gene Interaction (DGI) is crucial for drug discovery and personalized medicine. The continuous development of genomics and drug repositioning has brought increasing attention to the complex relations between drugs and genes. However, traditional biological experiments are time-consuming and costly, which makes it challenging to efficiently explore the multi-relational interactions between drugs and genes. Therefore, computational approaches aim to develop efficient schemes for predicting drug-gene relations to reduce the search space and experimental costs. Existing computational methods often suffer from data scarcity and poor generalization, which pose significant challenges for practical applications. To address these issues, we propose a novel multi-relation DGI prediction method based on molecular structure-driving and high-low-order attention denoising framework. Our approach captures molecular structural information through both atom and bond channels with a drug feature encoder. For network structure, we enhance both high- and low-order channels: the low-order channel leverages graph convolutional networks, while the high-order channel employs hypergraph-based message propagation. Additionally, we adopt consistency information loss and inter-channel attention mechanism to refine high- and low-order features. Experimental results on three drug-gene datasets demonstrate the superior performance of our model, particularly on sparse datasets DrugBank and DGIdb, with F1 improvements of 4.06% and 5.67%, respectively.

Accurate prediction of drug-target interactions (DTIs) is essential for advancing drug discovery and repurposing. However, the sparsity of DTI data limits the effectiveness of existing computational methods, which primarily focus on sparse DTI networks and have poor performance in aggregating information from neighboring nodes and representing isolated nodes within the network. In this study, we propose a novel deep learning framework, named GIAE-DTI, which considers cross-modal similarity of drugs and targets and constructs a heterogeneous network for DTI prediction. Firstly, the model calculates the cross-modal similarity of drugs and proteins from the relationships among drugs, proteins, diseases, and side effects, and performs similarity integration by taking the average. Then, a drug-target heterogeneous network is constructed, including drug-drug interactions, protein-protein interactions, and drug-target interactions processed by weighted K nearest known neighbors. In the heterogeneous network, a graph autoencoder based on a graph isomorphism network is employed for feature extraction, while a dual decoder is utilized to achieve better self-supervised learning, resulting in latent feature representations for drugs and targets. Finally, a deep neural network is employed to predict DTIs. The experimental results indicate that on the benchmark dataset, GIAE-DTI achieves AUC and AUPR scores of 0.9533 and 0.9619, respectively, in DTI prediction, outperforming the current state-of-the-art methods. Additionally, case studies on four 5-hydroxytryptamine receptor-related targets and five drugs related to mental diseases show the great potential of the proposed method in practical applications.

Hyperedges, as extensions of pairwise edges, can characterize higher-order relations among multiple individuals. Due to the necessity of hypergraph detection in practical systems, hyperedge prediction has become a frontier problem in complex networks. However, previous hyperedge prediction models encounter three challenges: (i) failing to predict dynamic and arbitrary-order hyperedges simultaneously, (ii) confusing higher-order and lower-order features together to propagate neighborhood information, and (iii) lacking the capability to learn physical evolution laws, which lead to poor performance of the models. To tackle these challenges, we propose D$^{3}$HP, aDual-viewDesynchronization hypergraph learning for arbitrary-orderDynamicHyperedgePrediction. Specifically, D$^{3}$HP extracts the dynamic higher-order and lower-order features of hyperedges separately through an elastic hypergraph neural network (EHGNN) and an alternate desynchronization graph convolutional network (ADGCN) at each time snapshot. EHGNN is designed to incrementally mine the implicit higher-order relations and propagate neighborhood information. Moreover, ADGCN aims to combine GCN with desynchronization learining to learn the physical evolution of lower-order relations and alleviate the over-smoothing problem. Further, we improve the prediction performance of the model by rationally fusing the features learned from the dual views. Extensive experiments on 8 dynamic higher-order networks demonstrate that D$^{3}$HP outperforms 14 state-of-the-art baselines.

Drug-gene interaction plays a crucial role in drug discovery and personalized medicine. Although existing methods have improved the accuracy of exploring multiple relationships between drugs and genes, there are still some limitations, such as susceptibility to data sparsity and poor generalization, which pose some challenges for practical applications. To address these challenges, we propose a novel Hierarchical Channels and Contrastive Learning (HCCL) framework in which drug feature extractor captures structural information of drug molecules from atom and bond channels. After obtaining the initial features of drugs and genes, we employ high-low-order channels to update them, where the low-order channel adopts graph convolutional networks while the high-order channel leverages hypergraph structures for message propagation. Finally, we adopt contrastive learning and inter-channel attention to fuse high-low-order features, which improves the robustness of the model and prevents feature information loss. Experimental results demonstrate the superior performance of HCCL.

Recently, higher order patterns have played an important role in network structure analysis. The simplices in higher order patterns enrich dynamic network modeling and provide strong structural feature information for feature learning. However, the disorder dynamic network with simplex patterns has not been organized and divided according to time windows. Besides, existing methods do not make full use of the feature information to predict the simplex patterns with higher orders. To address these issues, we propose a simplex pattern prediction method based on dynamic higher order path convolutional networks. First, we divide the dynamic higher order datasets into different network structures under continuous-time windows, which possess complete time information. Second, feature extraction is performed on the network structure of continuous-time windows through higher order path convolutional networks. Subsequently, we embed time nodes into feature encoding and obtain feature representations of simplex patterns through feature fusion. The obtained feature representations of simplices are recognized by a simplex pattern discriminator to predict the simplex patterns at different moments. Finally, compared to other dynamic graph representation learning algorithms, our proposed algorithm has significantly improved its performance in predicting simplex patterns on five real dynamic higher order datasets.

Identifying the optimal groups of users that are closely connected and satisfy some ranking criteria from an attributed social network attracts significant attention from both academia and industry. Skyline query processing, a multicriteria decision-making optimized technique, is recently embedded into cohesive subgraphs mining in graphs/social networks. However, the existing studies cannot capture the fuzzy property of connections between users in social networks. To fill this gap, in this article, we formulate a novel model of the skyline$(\lambda,k)$-cliques over a fuzzy attributed social network and develop a formal concept analysis (FCA)-based skyline$(\lambda,k)$-cliques identification algorithm. Specifically,$\lambda $can be regarded as a quality control parameter for measuring the stability of the cohesive groups. Extensive experimental results conducted on three real-world datasets demonstrate the effectiveness of the skyline$(\lambda,k)$-clique model in a fuzzy attributed social network. Furthermore, an illustrative example is executed for revealing the usefulness of our model. It is expected that our proposed skyline$(\lambda,k)$-clique model can be widely used in various graph-based computational social systems, such as optimal team formation in crowdsourcing, and group recommendation in social networks.