This paper introduces a novel approach for link prediction in social networks using hypergraph representation. The method involves modeling the network as a hypergraph, which allows for the representation of higher-order interactions between nodes, unlike traditional "node–edge" structures. The paper proposes the Learning Embedding based on Hyper-Motif of the Network (LEHMN) model, which uses hyper-motifs as hyper-nodes to enhance the representation of structural similarities between nodes. The model incorporates a depth and breadth motif random walk strategy to efficiently acquire node sequences, improving the accuracy of link prediction. The proposed method is tested on various datasets and outperforms state-of-the-art baselines, demonstrating its effectiveness in capturing complex relationships within social networks. The paper highlights the importance of considering higher-order interactions in network modeling and shows how hypergraphs can be used to represent these interactions more accurately. The LEHMN model uses a skip-gram model to learn embedding vectors based on node sequences, where sequences are extracted using random walk techniques. The model's ability to capture both node and hyper-node similarities makes it a powerful tool for link prediction in complex networks. The paper also discusses the limitations of traditional methods in capturing higher-order interactions and emphasizes the need for more sophisticated models that can handle these interactions. Overall, the paper presents a novel approach to link prediction in social networks that leverages hypergraph representation and hyper-motif structures to improve the accuracy and effectiveness of link prediction.This paper introduces a novel approach for link prediction in social networks using hypergraph representation. The method involves modeling the network as a hypergraph, which allows for the representation of higher-order interactions between nodes, unlike traditional "node–edge" structures. The paper proposes the Learning Embedding based on Hyper-Motif of the Network (LEHMN) model, which uses hyper-motifs as hyper-nodes to enhance the representation of structural similarities between nodes. The model incorporates a depth and breadth motif random walk strategy to efficiently acquire node sequences, improving the accuracy of link prediction. The proposed method is tested on various datasets and outperforms state-of-the-art baselines, demonstrating its effectiveness in capturing complex relationships within social networks. The paper highlights the importance of considering higher-order interactions in network modeling and shows how hypergraphs can be used to represent these interactions more accurately. The LEHMN model uses a skip-gram model to learn embedding vectors based on node sequences, where sequences are extracted using random walk techniques. The model's ability to capture both node and hyper-node similarities makes it a powerful tool for link prediction in complex networks. The paper also discusses the limitations of traditional methods in capturing higher-order interactions and emphasizes the need for more sophisticated models that can handle these interactions. Overall, the paper presents a novel approach to link prediction in social networks that leverages hypergraph representation and hyper-motif structures to improve the accuracy and effectiveness of link prediction.