Knowledge precedence networks: Mining progression patterns of scientific discoveries beyond prerequisites

Understanding how knowledge evolves through scientists’ career paths is essential for advancing education and innovation. This study constructs Knowledge Precedence Networks (KPNs) to uncover scientific progression patterns in real-world practice across 19 disciplines, analyzing the research trajectories of 4,969,403 scientists and 80 million publications from the OpenAlex dataset. We propose the CoCiTCD method, which integrates Co - Ci ting networks with T emporal C ommunity D etection to capture knowledge progression structures by identifying research communities, selecting representative concepts, and deriving temporal concept pairs. KPNs across Mathematics, Computer Science, and Engineering emphasize the critical role of foundational concepts in supporting advanced topics. For example, Algorithms bridge Mathematics and Computer Science, driving advancements in Artificial Intelligence and Data Science. We evaluate the alignment between KPNs for 303 concepts and theoretical prerequisite relations annotated by large language models, revealing how scientists engage with knowledge over time. The KPN attains a recall of 25.77% in best case, complemented by the citation-based KCN reaching 26.6%. This consistently low alignment indicates that empirical real-world topic transitions frequently diverge from theoretical prerequisite orderings. Furthermore, an AUC of 0.76 on our sample variational ROC curve underscores the robustness of our KPN approach in capturing the nuanced, innovative nature of knowledge progression. The KPNs provide valuable insights for research planning, learning path design, interdisciplinary collaboration, and understanding the hierarchical knowledge structure, thereby contributing to the Science of Science by uncovering real patterns of knowledge progression across disciplines.