In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

Recently, graph neural network (GNN) has emerged as a powerful representation learning tool for graph-structured data. However, most approaches are tailored for undirected graphs, neglecting the abundant information in the edges of directed graphs (digraphs). In fact, digraphs are widely applied in the real world and confirmed to address heterophily challenges. Despite recent advancements, existing spatial- and spectral-based DiGNNs have limitations due to their complex learning mechanisms and reliance on high-quality topology, resulting in low efficiency and unstable performance. To address these issues, we propose Directed Random Walk (DiRW), a plug-and-play strategy for most spatial-based DiGNNs and also an innovative model which offers a new digraph learning paradigm. Specifically, it utilizes a direction-aware path sampler optimized from the perspectives of walk probability, length, and number in a weight-free manner by considering node profiles and topologies. Building upon this, DiRW incorporates a node-wise learnable path aggregator for generalized node representations. Extensive experiments on 9 datasets demonstrate that DiRW: (1) enhances most spatial-based methods as a plug-and-play strategy; (2) achieves SOTA performance as a new digraph learning paradigm. The source code and data are available at https://github.com/dhsiuu/DiRW.

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.

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 16 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96%.

Scalable graph neural networks (GNNs) have emerged as a promising technique, which exhibits superior predictive performance and high running efficiency across numerous large-scale graph-based web applications. However, (i) Most scalable GNNs tend to treat all nodes with the same propagation rules, neglecting their topological uniqueness; (ii) Existing node-wise propagation optimization strategies are insufficient on web-scale graphs with intricate topology, where a full portrayal of nodes' local properties is required. Intuitively, different nodes in web-scale graphs possess distinct topological roles, and therefore propagating them indiscriminately or neglecting local contexts may compromise the quality of node representations. To address the above issues, we propose Adaptive Topology-aware Propagation (ATP), which reduces potential high-bias propagation and extracts structural patterns of each node in a scalable manner to improve running efficiency and predictive performance. Remarkably, ATP is crafted to be a plug-and-play node-wise propagation optimization strategy, allowing for offline execution independent of the graph learning process in a new perspective. Therefore, this approach can be seamlessly integrated into most scalable GNNs while remaining orthogonal to existing node-wise propagation optimization strategies. Extensive experiments on 12 datasets have demonstrated the effectiveness of ATP.

Most existing graph neural networks (GNNs) are limited to undirected graphs, whose restricted scope of the captured relational information hinders their expressive capabilities and deployment. Compared with undirected graphs, directed graphs (digraphs) fit the demand for modeling more complex topological systems by capturing more intricate relationships between nodes. While some directed GNNs have been introduced, their inspiration mainly comes from deep learning architectures, which lead to redundant complexity and computation, making them inapplicable to large-scale databases. To address these issues, we propose LightDiC, a scalable variant of the digraph convolution based on the magnetic Laplacian. Since topology-related computations are conducted solely during offline pre-processing, LightDiC achieves exceptional scalability, enabling downstream predictions to be trained separately without incurring recursive computational costs. Theoretical analysis shows that LightDiC achieves message passing based on the complex field, which corresponds to the proximal gradient descent process of the Dirichlet energy optimization function from the perspective of digraph signal denoising, ensuring its expressiveness. Experimental results demonstrate that LightDiC performs comparably well or even outperforms other SOTA methods in various downstream tasks, with fewer learnable parameters and higher efficiency.

Diversified recommendation systems have gained increasing popularity in recent years. Nowadays, the emerged graph neural networks (GNNs) have been used to improve the diversity performance. Although some progresses have been made, existing works purely focus on the user–item interactions and overlook the category information, which limits the capability to capture complex diversification among users or items and leads to poor performance. In this article, our target is to integrate full category information into user and item embeddings. To this end, we propose a diversified GNN-based recommendation systems diversified graph recommendation with contrastive learning (DCL). Specifically, we design three key components in our model: 1) the user–item interaction with category-related sampling enhances the interaction of unpopular items; 2) contrastive learning between users and categories shortens the distance of representations between users and their uninteracted categories; and 3) contrastive learning between items and categories diverges the distance of representations between items and their corresponding categories. By applying these three modules, we build a multitask training framework to achieve a balance between accuracy and diversity. Experiments on real-world datasets show that our proposed DCL achieves optimal diversity while paying a little price for accuracy.