Abstract: The study of higher-order structures, which refer to subnetworks within a network, is a crucial research topic in network science. In recent years, although the research on higher-order structures has been increasing, there has been relatively little research on the internal connections between higher-order structures. In light of conventional association rules, the evaluation criteria of association rules between higher-order structures are defined, and a general algorithm framework for effectively mining these association rules is proposed. The proposed approach has been applyed to mine association rules among three-order structures in six real-world networks. The results demonstrate strong association rules between higher-order structures in real-world networks, as well as variations in these rules across different networks. Additionally, we apply strong association rules to link prediction, resulting in a new link prediction method. This method outperforms the baseline methods in four real networks.