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.

The utilization of graph neural networks in heterogeneous networks has been rapidly increasing in recent years. The topological structure, fundamental to the nature of graphs, is often claimed to be jointly addressed with attribute information by most heterogeneous graph neural network (HGNN) approaches. However, this assertion lacks sufficient empirical validation. We empirically challenge these claims within existing evaluation frameworks. We propose a straightforward multi-layer perceptron (MLP) based model which relies solely on adjacency relationships for feature aggregation, without fully exploiting the graph's intricate topological structures. Unexpectedly, the model achieved nearly state-of-the-art performance on several real-world datasets. This discrepancy indicates that current evaluation protocols contain systemic biases and often fail to distinguish superficial adjacency exploitation from genuine structural pattern learning. It also points to the need for future benchmark datasets and metrics that more faithfully reflect the real requirements of topological learning. We hope this work stimulates further research into the role and significance of topological information in HGNNs.

Most network embedding (NE) methods are either based on the proximity for community-guided tasks or on the structural similarity for role-oriented tasks. While being prevalent and effective, there still exists some potential issues that need further attention: 1) community and role are always regarded as orthogonal problems. They have rarely been combined to model the latent structures within the complex network. However, the generation of the network is usually jointly driven by these two mechanisms; and 2) few works study the interaction between roles or communities, which leads to the generation process of the network cannot being effectively modeled. To solve these problems, we propose a unified network embedding framework via mutual fusion of community and role (UMFCR). We combine the Gaussian mixture model (GMM) with a variational graph auto-encoder to generate node embeddings and discover the membership distribution of each node. An elaborate fusion pattern is then designed to produce the generation process for each link from the perspective of both community and role. The promising experimental results on real-world data demonstrate the necessity of fusing these two mechanisms and the superior performance of the model on different network tasks.

Temporal interaction graphs (TIGs), defined by sequences of timestamped interaction events, have become ubiquitous in real-world applications due to their capability to model complex dynamic system behaviors. As a result, temporal interaction graph representation learning (TIGRL) has garnered significant attention in recent years. TIGRL aims to embed nodes in TIGs into low-dimensional representations that effectively preserve both structural and temporal information, thereby enhancing the performance of downstream tasks such as classification, prediction, and clustering within constantly evolving data environments. In this paper, we begin by introducing the foundational concepts of TIGs and emphasizing the critical role of temporal dependencies. We then propose a comprehensive taxonomy of state-of-the-art TIGRL methods, systematically categorizing them based on the types of information utilized during the learning process to address the unique challenges inherent to TIGs. To facilitate further research and practical applications, we curate the source of datasets and benchmarks, providing valuable resources for empirical investigations. Finally, we examine key open challenges and explore promising research directions in TIGRL, laying the groundwork for future advancements that have the potential to shape the evolution of this field.

The pre-training and fine-tuning methods have gained widespread attention in the field of heterogeneous graph neural networks due to their ability to leverage large amounts of unlabeled data during the pre-training phase, allowing the model to learn rich structural features. However, these methods face the issue of a mismatch between the pre-trained model and downstream tasks, leading to suboptimal performance in certain application scenarios. Prompt learning methods have emerged as a new direction in heterogeneous graph tasks, as they allow flexible adaptation of task representations to address target inconsistency. Building on this idea, this paper proposes a novel multi-task prompt framework for the heterogeneous graph domain, named HGMP. First, to bridge the gap between the pre-trained model and downstream tasks, we reformulate all downstream tasks into a unified graph-level task format. Next, we address the limitations of existing graph prompt learning methods, which struggle to integrate contrastive pre-training strategies in the heterogeneous graph domain. We design a graph-level contrastive pre-training strategy to better leverage heterogeneous information and enhance performance in multi-task scenarios. Finally, we introduce heterogeneous feature prompts, which enhance model performance by refining the representation of input graph features. Experimental results on public datasets show that our proposed method adapts well to various tasks and significantly outperforms baseline methods.

The Heterogeneous Information Network (HIN) stands out as a prominent tool for depicting interactions in real-world systems. Recently, representation learning on HINs has attracted significant attention, as the structured and compact output embeddings offer great convenience for network analysis and graph machine learning tasks. While existing HIN representation learning methods excel in supervised training or direct proximity reconstruction, yielding satisfactory performance in tasks like node clustering and classification, they often overlook the critical HIN generative process characterized by numerous events. As a result, these methods fail to preserve the higher-order interactions among the nodes and predict potential links in HINs. To address these limitations, we propose a Contrastive Learning method via Events on Heterogeneous Information Networks (CLEH). CLEH delineates the generative process from the local structure (nodes) to the higher-order structure (events) in HINs. We design a novel event-level contrastive learning procedure, endowing representations with the capability to capture higher-order relations among nodes. Moreover, CLEH leverages a normalizing flow model as the encoder to enhance the expressiveness of embeddings. Experimental results on HIN datasets demonstrate the significant superiority of CLEH in link prediction compared to popular baselines.

Graph contrastive learning (GCL), as a popular self-supervised learning technique, has demonstrated promising capability in learning discriminative representations for diverse downstream tasks. A large body of GCL frameworks mainly work on graphs formed under homophily effect, i.e., similar nodes tend to connect with each other. In their design, the augmentation and aggregation are usually conducted indiscriminately on edges, ignoring the existence of heterophilic edges that connect dissimilar nodes. Therefore, the efficacy of GCL could greatly deteriorate on heterophilic graphs, verified by our analysis: GCL on a mixture of homophilic and heterophilic edges will generate representations that are indistinguishable across different classes in the embedding space. To address this challenge, we propose a novel GCL framework via interventional view generation. Specifically, we generate homophilic and heterophilic views through counterfactual intervention, which targets on disentangling homophilic and heterophilic structure from the original graph, such that we can capture their corresponding information using separate filters in the contrastive learning process. Since the homophilic view and the heterophilic view present different frequency signals, they are further encoded via a low-pass and a high-pass filter respectively. Extensive experiments on multiple benchmark datasets demonstrate the effectiveness of our design. Our proposed framework achieves a remarkably improved downstream performance on graphs with high heterophily while maintaining a comparable ability in learning homophilic graphs. A comprehensive study also verifies the necessity of individual designs in our framework.

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.

Roles are defined as the equivalent classes of isomorphic nodes in the network. They focus on the local connective patterns and describe the structural similarities between nodes, and learning role-based network embeddings can help to recognize identities or functions of entities in real-world networks. This field has been studied over the past decades, however, the existing role-based network embedding methods all concentrate too much on distinguishing node structures and ignore that nodes can belong to different roles even if they have the same local structures. Not only the classical network structure can influence the role of node, but also the emergence of different type of relationship between nodes has impact to it. We believe that roles are influenced by multiple independent factors, and nodes in the same roles should possess both similar local structures and entangled patterns with neighbors hidden in each factor, but most of the existing methods did not clearly point out this challenge. Therefore, we propose a disentangled framework based on graph neural networks to simultaneously model the local structures and interactive relationships in multiple factors to generate role-oriented network embeddings. We design a novel role-aware neighbor choosing mechanism to assign each neighbor a different interactive weight for each latent factor, which can measure its influence on roles. We conduct experiments on synthetic and real-world networks, and the results demonstrate the superiority and effectiveness of our model.

Capturing structural similarity has been a hot topic in the field of network embedding (NE) recently due to its great help in understanding node functions and behaviors. However, existing works have paid very much attention to learning structures on homogeneous networks, while the related study on heterogeneous networks is still void. In this article, we try to take the first step for representation learning on heterostructures, which is very challenging due to their highly diverse combinations of node types and underlying structures. To effectively distinguish diverse heterostructures, we first propose a theoretically guaranteed technique called heterogeneous anonymous walk (HAW) and give two more applicable variants. Then, we devise the HAW embedding (HAWE) and its variants in a data-driven manner to circumvent using an extremely large number of possible walks and train embeddings by predicting occurring walks in the neighborhood of each node. Finally, we design and apply extensive and illustrative experiments on synthetic and real-world networks to build a benchmark on heterostructure learning and evaluate the effectiveness of our methods. The results demonstrate our methods achieve outstanding performance compared with both homogeneous and heterogeneous classic methods and can be applied on large-scale networks.

Recently, network embedding (NE) is an amazing research point in complex networks and devoted to a variety of tasks. Nearly, all the methods and models of NE are based on the local, high-order, or global similarity of the networks, and few studies have focused on the role discovery or structural similarity, which is of great significance in spreading dynamics and network theory. Meanwhile, existing NE models for role discovery suffer from two limitations, that is: 1) they fail to model the varying dependencies between each node and its neighbor nodes and 2) they cannot capture the effective node features which are helpful to role discovery, which makes these methods ineffective when applied to the role discovery task. To solve the above problems of NE for role discovery or structural similarity, we propose a unified deep learning framework, called RDAA, which can effectively represent features of nodes and benefit the Role Discovery-guided NE with a deep autoencoder, while modeling the local links with an Attention mechanism. In addition, we design an elaborately binding technique to combine both parts and optimize the framework in a unified way. We conduct different experiments, including visualization, role classification, role discovery, and running time compared to popular NE methods for both proximity and structural similarity. The RDAA has better performance on all the datasets and achieves good tradeoffs.

Recently, Network Embedding (NE) has become one of the most attractive research topics in machine learning and data mining. NE approaches have achieved promising performance in various graph mining tasks including link prediction and node clustering and classification. A wide variety of NE methods focus on the proximity of networks, they learn community-oriented embedding for each node, where the corresponding representations are similar if two nodes are closer to each other in the network. Meanwhile, there is another type of structural similarity, i.e., role-based similarity, which is completely different from and complementary to the proximity. In order to preserve the role-based structural similarity, the problem of role-oriented NE is raised. However, compared to the community-oriented NE, there are only a few role-oriented embedding approaches proposed recently. Although less explored, considering the importance of roles in analyzing networks and many applications that role-oriented NE can shed light on, it is necessary and timely to provide a comprehensive overview of existing role-oriented NE methods. In this review, we first clarify the differences between community-oriented and role-oriented network embedding. Afterward, we propose a general framework for understanding role-oriented NE and a two-level categorization to better classify existing methods. Then, we select some representative methods according to the proposed categorization and briefly introduce them by discussing their motivation, development, and differences. Moreover, we conduct comprehensive experiments to empirically evaluate these methods on a variety of role-related tasks including node classification and clustering (role discovery), top-k similarity search, and visualization using some widely used synthetic and real-world datasets. Finally, we further discuss the research trend of role-oriented NE from the perspective of applications and point out some potential future directions.

Network representation learning or embedding aims to project the network into a low-dimensional space that can be devoted to different network tasks. Temporal networks are an important type of network whose topological structure changes over time. Compared with methods on static networks, temporal network embedding (TNE) methods are facing three challenges: 1) it cannot describe the temporal dependence across network snapshots; 2) the node embedding in the latent space fails to indicate changes in the network topology; and 3) it cannot avoid a lot of redundant computation via parameter inheritance on a series of snapshots. To overcome these problems, we propose a novel TNE method named temporal network embedding method based on the VAE framework (TVAE), which is based on a variational autoencoder (VAE) to capture the evolution of temporal networks for link prediction. It not only generates low-dimensional embedding vectors for nodes but also preserves the dynamic nonlinear features of temporal networks. Through the combination of a self-attention mechanism and recurrent neural networks, TVAE can update node representations and keep the temporal dependence of vectors over time. We utilize parameter inheritance to keep the new embedding close to the previous one, rather than explicitly using regularization, and thus, it is effective for large-scale networks. We evaluate our model and several baselines on synthetic data sets and real-world networks. The experimental results demonstrate that TVAE has superior performance and lower time cost compared with the baselines.

Roles of nodes are defined as classes of equivalent nodes. Nodes that have similar local connective patterns may share the same role. As a complementary concept of community, role can also help to recognize real-world entities. For example, it can denote identity or function in social networks. Role has been studied over the past decades, and learning role-based network representations is crucial to many downstream tasks. The important step for role-based network embedding method is extracting features to measure structural similarity instead of proximity. Although some methods have been developed to capture role features to learn structural similarities between nodes, they all design these features of fixed types, such as the global, local, and higher-order features. These features can only represent a certain type of structure, and it is very difficult to model the complex relationship between different scale features in the field of role-based network embedding. Therefore, we propose a novel role-oriented network embedding framework based on adversarial learning between higher-order and local features (ARHOL) to generate powerful role-based node representations. The higher-order features are discrete so we leverage the Auto-Encoder on them to obtain continuous representations. Then we apply the GIN on its outputs to aggregate local information. Finally, we consider the GIN as the generator and design an adversarial game between local features and GIN outputs to integrate these two aspects of features, which can enhance each other and improve the robustness. The extensive experiments on real-world networks demonstrate the superiority and efficiency of our model, and prove the effectiveness of integrating higher-order and local features.

Role-based network embedding methods aim to preserve node-centric connectivity patterns, which are expressions of node roles, into low-dimensional vectors. However, almost all the existing methods are designed for capturing a relaxation of automorphic equivalence or regular equivalence. They may be good at structure identification but could show poorer performance on role identification. Because automorphic equivalence and regular equivalence strictly tie the role of a node to the identities of all its neighbors. To mitigate this problem, we construct a framework called Curvature-based Network Embedding with Stochastic Equivalence (CNESE) to embed stochastic equivalence. More specifically, we estimate the role distribution of nodes based on discrete Ricci curvature for its excellent ability to concisely representing local topology. We use a Variational Auto-Encoder to generate embeddings while a degree-guided regularizer and a contrastive learning regularizer are leveraged to improving both its robustness and discrimination ability. The effectiveness of our proposed CNESE is demonstrated by extensive experiments on real-world networks.