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.

Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. Existing methods employ learnable graph structures and graph neural networks to explicitly model the spatial dependencies between variables. However, these methods are primarily based on prediction or reconstruction tasks, which can only learn similarity relationships between sequence embeddings and lack interpretability in how graph structures affect time series evolution. In this paper, we designed a framework that models spatial dependencies using interpretable causal relationships and detects anomalies through changes in causal patterns. Specifically, we propose a method to dynamically discover Granger causality using gradients in nonlinear deep predictors and employ a simple sparsification strategy to obtain a Granger causality graph, detecting anomalies from a causal perspective. Experiments on real-world datasets demonstrate that the proposed model achieves more accurate anomaly detection compared to baseline methods.

Graph representation learning (GRL) has emerged as an effective technique for modeling graph-structured data. When modeling heterogeneity and dynamics in real-world complex networks, GRL methods designed for complex heterogeneous temporal graphs (HTGs) have been proposed and have achieved successful applications in various fields. However, most existing GRL methods mainly focus on preserving the low-order topology information while ignoring higher-order group interaction relationships, which are more consistent with real-world networks. In addition, most existing hypergraph methods can only model static homogeneous graphs, limiting their ability to model high-order interactions in HTGs. Therefore, to simultaneously enable the GRL model to capture high-order interaction relationships in HTGs, we first propose a formal definition of heterogeneous temporal hypergraphs and P-uniform heterogeneous hyperedge construction algorithm that does not rely on additional information. Then, a novel Heterogeneous Temporal HyperGraph Neural network (HTHGN), is proposed to fully capture higher-order interactions in HTGs. HTHGN contains a hierarchical attention mechanism module that simultaneously performs temporal message-passing between heterogeneous nodes and hyperedges to capture rich semantics in a wider receptive field brought by hyperedges. Furthermore, HTHGN performs contrastive learning by maximizing the consistency between low-order correlated heterogeneous node pairs on HTG to avoid the low-order structural ambiguity issue. Detailed experimental results on three real-world HTG datasets verify the effectiveness of the proposed HTHGN for modeling high-order interactions in HTGs and demonstrate significant performance improvements.

Although contrastive self-supervised learning (SSL) on dynamic graphs has made significant success, the issue of heavy reliance on data augmentation and training tricks has been a persistent pain point. Generative SSL, especially masked autoencoders (MAEs) have recently produced promising results and can avoid these issues. However, the research on MAE in dynamic graphs remains largely unexplored due to the following challenges: 1) how to design an effective masking strategy for dynamic graphs? and 2) how to design a decoder to retain temporal dependency when graphs are perturbed? In this article, we propose DVGMAE, a novel dynamic variational graph masked autoencoder model to solve these challenges. DVGMAE simultaneously captures the evolving behaviors and topological features via an innovative masking strategy and an elaborate decoder. Specifically, we first implement a temporal-aware masking strategy on the edges of each snapshot based on the updated probabilities derived from historical mask information. This strategy mitigates potential masking bias in dynamic graphs. We then design a globally enhanced decoder to recover the temporal and spatial information of each snapshot. Extensive experiments demonstrate that DVGMAE outperforms the existing state-of-the-art on various tasks across different datasets.

Generative self-supervised learning (SSL), especially masked autoencoders (MAE), has greatly succeeded and garnered substantial research interest in graph machine learning. However, the research of MAE in dynamic graphs is still scant. This gap is primarily due to the dynamic graph not only possessing topological structure information but also encapsulating temporal evolution dependency. Applying a random masking strategy which most MAE methods adopt to dynamic graphs will remove the crucial subgraph that guides the evolution of dynamic graphs, resulting in the loss of crucial spatio-temporal information in node representations. To bridge this gap, in this paper, we propose a novel Informative Subgraphs Aware Masked Auto-Encoder in Dynamic Graph, namely DyGIS. Specifically, we introduce a constrained probabilistic generative model to generate informative subgraphs that guide the evolution of dynamic graphs, successfully alleviating the issue of missing dynamic evolution subgraphs. The informative subgraph identified by DyGIS will serve as the input of dynamic graph masked autoencoder (DGMAE), effectively ensuring the integrity of the evolutionary spatio-temporal information within dynamic graphs. Extensive experiments on eleven datasets demonstrate that DyGIS achieves state-of-the-art performance across multiple tasks.

Heterogeneous graphs (HGs) with multiple entity and relation types are common in real-world networks. Heterogeneous graph neural networks (HGNNs) have shown promise for learning HG representations. However, most HGNNs are designed for static HGs and are not compatible with heterogeneous temporal graphs (HTGs). A few existing works have focused on HTG representation learning but they care more about how to capture the dynamic evolutions and less about their compatibility with those well-designed static HGNNs. They also handle graph structure and temporal dependency learning separately, ignoring that HTG evolutions are influenced by both nodes and relationships. To address this, we propose HGN2T, a simple and general framework that makes static HGNNs compatible with HTGs. HGN2T is plug-and-play, enabling static HGNNs to leverage their graph structure learning strengths. To capture the relationship-influenced evolutions, we design a special mechanism coupling both the HGNN and sequential model. Finally, through joint optimization by both detection and prediction tasks, the learned representations can fully capture temporal dependencies from historical information. We conduct several empirical evaluation tasks, and the results show our HGN2T can adapt static HGNNs to HTGs and overperform existing methods for HTGs.

Network embedding is an important class of link prediction methods, which can use the distance between learned low-dimensional node representations to characterize the similarity between nodes. Traditional network embedding methods focus on single-layer networks, while in reality, a large part of complex networks are not isolated, but interdependent and interrelated, forming multiplex complex networks. Also, how to effectively exploit layer correlations in multiplex networks to learn more robust and valuable representations, to improve link prediction performance, has been a hot research topic in the field of complex network analysis. However, previous studies mainly focus on inferring intralinks in each layer of complex networks or anchor links among layers. Another issue that has not been discussed is how to predict potential links or reconstruct the network in unobserved relations based on existing multiplex networks. To this issue, we define a novel inductive link prediction problem in multiplex networks, in which most existing multichannel network embedding methods fail to solve. This is either because they only emphasize the specific structure information of an individual layer or only capture the common information for all layers. To effectively address this problem, we propose a novel embedding method termed interactive learning across relations (ILAR), to capture and fully exploit the multiple relations and complex layer correlations in multiplex networks. We leverage two convolutional modules and ILAR to capture the sufficient complementary and correlations in multiplex networks. Moreover, during interactive learning, a disparity constraint is introduced, which enforces the features encoded from two convolutional modules to be different and prevents information redundancy. Finally, the extensive experiments in several real-world datasets show that our model can significantly outperform the existing state-of-the-art network embedding methods on the novel link prediction problem in multiplex networks.

Change point detection in dynamic networks aims to detect the points of sudden change or abnormal events within the network. It has garnered substantial interest from researchers due to its potential to enhance the stability and reliability of real-world networks. Most change point detection methods are based on statistical characteristics and phased training, and some methods are required to set the percent of change points. Meanwhile, existing methods for change point detection suffer from two limitations. On one hand, they struggle to extract snapshot features that are crucial for accurate change point detection, thereby limiting their overall effectiveness. On the other hand, they are typically tailored for specific network types and lack the versatility to adapt to networks of varying scales. To solve these issues, we propose a novel unified end-to-end framework called Variational Graph Gaussian Mixture model (VGGM) for change point detection in dynamic networks. Specifically, VGGM combines Variational Graph Auto-Encoder (VGAE) and Gaussian Mixture Model (GMM) through joint training, incorporating a Mixture-of-Gaussians prior to model dynamic networks. This approach yields highly effective snapshot embeddings via VGAE and a dedicated readout function, while automating change point detection through GMM. The experimental results, conducted on both real-world and synthetic datasets, clearly demonstrate the superiority of our model in comparison to the current state-of-the-art methods for change point detection.

For the sake of privacy, encrypting the content shared on the Internet is becoming popular. However, it brings a nontrivial challenge in regulating the illicit shared content (e.g., viruses, rumors, malicious code, etc.). To deal with it, lots of schemes have been proposed, which mainly rely on a third-party—regulatory authority (RA), to perform auditing, regulating or supervising exclusively. Although these schemes mitigate the problem of illicit shared content, they still suffer from the following two issues. On one hand, relying on a single RA alone may lead to the serious problems of injustice and inadequate regulating. On the other hand, users’ privacy is violated since an independent RA unconditionally inspects all the files shared by users. Therefore, we propose a joint regulating scheme (JRS) for secretly shared content based on threshold secret sharing algorithm and blockchain technology. To make the censor activities democratic and public, they are authorized by both the RAs and blockchain miners during which two threshold secret sharing algorithms are applied. Further, only the suspicious users (or files) are censored and the whole process is recorded as blockchain transactions to balance the user privacy and censoring fairness. At last, the results of security and performance analysis show that JRS can resist the known attacks and the cost is acceptable in practice.

Security issues in networked control systems (NCSs) have received increasing attention in recent years. However, security protection often requires extra energy consumption, computational overhead, and time delays, which could adversely affect the real-time and energy-limited system. In this paper, random cryptographic protection is implemented. It is less expensive with respect to computational overhead, time, and energy consumption, compared with persistent cryptographic protection. Under the consideration of weak attackers who have little system knowledge, ungenerous attacking capability and the desire for stealthiness and random zero-measurement attacks are introduced as the malicious modification of measurements into zero signals. NCS is modeled as a stochastic system with two correlated Bernoulli distributed stochastic variables for implementation of random cryptographic protection and occurrence of random zero-measurement attacks; the stochastic stability can be analyzed using a linear matrix inequality (LMI) approach. The proposed stochastic stability analysis can help determine the proper probability of running random cryptographic protection against random zero-measurement attacks with a certain probability. Finally, a simulation example is presented based on a vertical take-off and landing (VTOL) system. The results show the effectiveness, robustness, and application of the proposed method, and are helpful in choosing the proper protection mechanism taking into account the time delay and in determining the system sampling period to increase the resistance against such attacks.