The knowledge graph (KG) is an efficient form of knowledge organization and expression, providing prior knowledge support for various downstream tasks, and has received extensive attention in natural language processing. However, existing large-scale KGs have many hidden facts that need to be discovered. How to effectively use the structure information of KG is an important research direction of knowledge reasoning. Structure-Information-based reasoning over the knowledge graph is a technique used to find the missing facts by the structure information of KG. This survey summarizes the methods and applications of Structure-Information-based reasoning and hopes to be helpful to the research in this field. First, we introduced the definition of knowledge reasoning and the conceptual description of related tasks. Then, we reviewed the methods of Structure-Information-based reasoning. Specifically, we categorized them into four representative classes: PRA-based reasoning, Path-Embedding-based reasoning, RL-based reasoning, and GNN-based reasoning. We compared the motivations and details between practices in the same category. After that, we described the application of Structure-Information-based knowledge reasoning in the Knowledge Graph Completion, Question Answering System, Recommendation System, and other fields. Finally, we discussed the future research directions of Structure-Information-based reasoning.