This paper presents a novel approach to link prediction in network-structured data by learning a heuristic from local subgraphs using graph neural networks (GNNs). Link prediction aims to determine the likelihood of a link between two nodes in a network. Traditional heuristics, such as common neighbors and Katz index, have been widely used due to their simplicity and interpretability, but they rely on strong assumptions that may not hold in all network types. To address this limitation, the authors propose a new framework called SEAL, which learns graph structure features from local enclosing subgraphs. The paper introduces a theoretical foundation for link prediction heuristics, known as the γ-decaying heuristic theory. This theory unifies various high-order heuristics and shows that they can be effectively approximated from local subgraphs. The authors demonstrate that high-order heuristics, such as Katz, rooted PageRank, and SimRank, can be represented in a γ-decaying form, allowing them to be approximated with a small number of hops in the enclosing subgraph. The SEAL framework is designed to learn general graph structure features from local subgraphs, incorporating both latent and explicit node features. It uses a GNN to extract features from the subgraphs and learns a function that maps these features to the likelihood of a link. SEAL outperforms existing heuristic methods, latent feature methods, and network embedding techniques in various experiments, showing its effectiveness in link prediction tasks. The paper also discusses the importance of node labeling in the SEAL framework, which helps in capturing the structural importance of nodes within the subgraph. Additionally, the framework incorporates negative injection to improve the learning process by including both positive and negative links in the training data. Overall, the study provides a theoretical and practical foundation for learning link prediction heuristics from local subgraphs, demonstrating that such an approach can achieve strong performance in a wide range of network types.This paper presents a novel approach to link prediction in network-structured data by learning a heuristic from local subgraphs using graph neural networks (GNNs). Link prediction aims to determine the likelihood of a link between two nodes in a network. Traditional heuristics, such as common neighbors and Katz index, have been widely used due to their simplicity and interpretability, but they rely on strong assumptions that may not hold in all network types. To address this limitation, the authors propose a new framework called SEAL, which learns graph structure features from local enclosing subgraphs. The paper introduces a theoretical foundation for link prediction heuristics, known as the γ-decaying heuristic theory. This theory unifies various high-order heuristics and shows that they can be effectively approximated from local subgraphs. The authors demonstrate that high-order heuristics, such as Katz, rooted PageRank, and SimRank, can be represented in a γ-decaying form, allowing them to be approximated with a small number of hops in the enclosing subgraph. The SEAL framework is designed to learn general graph structure features from local subgraphs, incorporating both latent and explicit node features. It uses a GNN to extract features from the subgraphs and learns a function that maps these features to the likelihood of a link. SEAL outperforms existing heuristic methods, latent feature methods, and network embedding techniques in various experiments, showing its effectiveness in link prediction tasks. The paper also discusses the importance of node labeling in the SEAL framework, which helps in capturing the structural importance of nodes within the subgraph. Additionally, the framework incorporates negative injection to improve the learning process by including both positive and negative links in the training data. Overall, the study provides a theoretical and practical foundation for learning link prediction heuristics from local subgraphs, demonstrating that such an approach can achieve strong performance in a wide range of network types.