## 1 Introduction  
With the advent of the big data era, the Internet has become a major source of information collection in various fields, including social networks [1], shopping networks [2], protein networks [3], and more. The information within these networks often exhibits large-scale and complex topological structures. Notably, graph-structured data pervades in representing the relationships between interacting entities. Moreover, graphs have become an important data form for link prediction tasks [4], which involve predicting the missing relationships between entity pairs across different timelines. As the volume of graph-structured data continues to grow, researchers constantly grapple with issues related to predictive performance and computational cost. Approaches range from simple, easy-to-implement heuristic methods to the use of graph neural networks, which automatically learn complex patterns within the graph structure and manage large-scale graph data. All these methods require extensive sampling and training to enhance model predictive performance. However, as the volume of network data continues to surge, traditional prediction methods face challenges in computation and storage when dealing with large-scale data. To address the difficulties brought about by massive sampling and training, one potential solution lies in the use of subgraph-based methods to reduce computational overhead in large-scale graph structures. By focusing only on the subgraphs around the target nodes, the complexity of sampling and training can be significantly reduced, which in turn speeds up model training and improves prediction efficiency. For link prediction problems in large-scale recommendation systems, the Pinterest SAGE (PinSage) [5] model employs subgraph sampling and graph neural network models for representation learning. Empirical evidence has shown that subgraph-based methods have achieved commendable performance in link prediction tasks within recommendation systems. Similarly, the Graph WaveNet [6] model uses subgraph-based random walk sampling and convolution operations to model spatiotemporal graph data, capturing complex patterns and dynamic changes effectively, leading to superior performance. Consequently, subgraph-based prediction methods emerge as the optimal solution. In order to further alleviate the challenges associated with processing large-scale graph-structured data, a sparse subgraph sampling approach is employed for prediction tasks. This sampling method retains crucial structural information around the target nodes while reducing computational costs in large-scale graph structures. GNNs [7,8] have been proven to be an effective method for handling large-scale graph-structured data and are widely used in various tasks, such as node classification [9], graph classification [10], and link prediction. Early GNNs tended to use shallow encoders, where latent nodes were represented through random walks for learning, followed by the assessment of link probabilities based on the latent representations of the two endpoint nodes. However, due to the incompatibility between node features and inductive settings, the ability to train using all nodes was hindered. The advent of message-passing graph neural networks addressed these issues. GraphSAGE [11] serves to learn node representations in graph-structured data, taking better advantage of node features and proving more suitable for inductive settings. Therefore, it partially addresses the limitations of early GNNs. GraphSAGE is detailed in [12], which outlines its basic principles and key components. Firstly, GraphSAGE learns node representations by aggregating over the subgraphs of each node's neighbors. Secondly, detailed analysis is provided for applications in different domains. Lastly, experiments and results demonstrate the performance and effectiveness of the GraphSAGE model in specific tasks. Therefore, GraphSAGE has facilitated research on various downstream tasks, such as link prediction, node classification, and graph classification.