Practical real-world scenarios such as the Internet, social networks, and biological networks present the challenges of data scarcity and complex correlations, which limit the applications of artificial intelligence. The graph structure is a typical tool used to formulate such correlations, it is incapable of modeling high-order correlations among different objects in systems; thus, the graph structure cannot fully convey the intricate correlations among objects. Confronted with the aforementioned two challenges, hypergraph computation models high-order correlations among data, knowledge, and rules through hyperedges and leverages these high-order correlations to enhance the data. Additionally, hypergraph computation achieves collaborative computation using data and high-order correlations, thereby offering greater modeling flexibility. In particular, we introduce three types of hypergraph computation methods: ① hypergraph structure modeling, ② hypergraph semantic computing, and ③ efficient hypergraph computing. We then specify how to adopt hypergraph computation in practice by focusing on specific tasks such as three-dimensional (3D) object recognition, revealing that hypergraph computation can reduce the data requirement by 80% while achieving comparable performance or improve the performance by 52% given the same data, compared with a traditional data-based method. A comprehensive overview of the applications of hypergraph computation in diverse domains, such as intelligent medicine and computer vision, is also provided. Finally, we introduce an open-source deep learning library, DeepHypergraph (DHG), which can serve as a tool for the practical usage of hypergraph computation.

• Hypergraph computation is a methodology for modeling complex high-order correlations.

• Hypergraph structure modeling, semantic computing, and efficient computing are introduced.

• The applications of hypergraph computation in diverse domains are summarized.

• An open-source library DHG for learning hypergraph neural networks is introduced.