Towards Data-centric Machine Learning on Directed Graphs: a Survey

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 it into undirected formats and emphasizes model designs. This approach is inherently constrained in real-world applications due to inevitable information loss in simple undirected graphs and data-driven model optimization dilemmas associated with exceeding the upper bounds of 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 its 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.

DiRW: Path-Aware Digraph Learning for Heterophily

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 embedded in the edges of directed graphs (digraphs). In fact, digraphs are widely applied in the real world (e.g., social networks and recommendations) and are also confirmed to offer a new perspective for addressing topological heterophily challenges (i.e., connected nodes have complex patterns of feature distribution or labels). Despite recent significant advancements in DiGNNs, existing spatial- and spectral-based methods have inherent limitations due to the complex learning mechanisms and reliance on high-quality topology, leading to low efficiency and unstable performance. To address these issues, we propose Directed Random Walk (DiRW), which can be viewed as a plug-and-play strategy or an innovative neural architecture that provides a guidance or new learning paradigm for most spatial-based methods or digraphs. Specifically, DiRW incorporates 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 topological structure. Building upon this, DiRW utilizes a node-wise learnable path aggregator for generalized messages obtained by our proposed adaptive walkers to represent the current node. 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.

Rethinking Node-wise Propagation for Large-scale Graph Learning

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 in graphs 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 neglect local contexts may compromise the quality of node representations. This intricate topology in web-scale graphs cannot be matched by small-scale scenarios. To address the above issues, we propose \textbf{A}daptive \textbf{T}opology-aware \textbf{P}ropagation (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 remain orthogonal to existing node-wise propagation optimization strategies. Extensive experiments on 12 datasets, including the most representative large-scale ogbn-papers100M, have demonstrated the effectiveness of ATP. Specifically, ATP has proven to be efficient in improving the performance of prevalent scalable GNNs for semi-supervised node classification while addressing redundant computational costs.

LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning

Most existing graph neural networks (GNNs) are limited to undirected graphs, whose restricted scope of the captured relational information hinders their expressive capabilities and deployments in real-world scenarios. Compared with undirected graphs, directed graphs (digraphs) fit the demand for modeling more complex topological systems by capturing more intricate relationships between nodes, such as formulating transportation and financial networks. 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 utilizes directed information to achieve 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 training efficiency. Notably, LightDiC is the first DiGNN to provide satisfactory results in the most representative large-scale database (ogbn-papers100M).

Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification

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 \underline{A}daptively \underline{M}odeling the natural directed graphs as the \underline{U}ndirected or \underline{D}irected graph to maximize the benefits from subsequent graph learning. Furthermore, we propose \underline{A}daptive \underline{D}irected \underline{P}attern \underline{A}ggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 14 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96\%.