Understanding a complex system of relationships between courses is of great importance for the university's educational mission. This paper is dedicated to the study of course-prerequisite networks (CPNs), where nodes represent courses and directed links represent the formal prerequisite relationships between them. The main goal of CPNs is to model interactions between courses, represent the flow of knowledge in academic curricula, and serve as a key tool for visualizing, analyzing, and optimizing complex curricula. First, we consider several classical centrality measures, discuss their meaning in the context of CPNs, and use them for the identification of important courses. Next, we describe the hierarchical structure of a CPN using the topological stratification of the network. Finally, we perform the interdependence analysis, which allows to quantify the strength of knowledge flow between university divisions and helps to identify the most intradependent, influential, and interdisciplinary areas of study. We discuss how course-prerequisite networks can be used by students, faculty, and administrators for detecting important courses, improving existing and creating new courses, navigating complex curricula, allocating teaching resources, increasing interdisciplinary interactions between departments, revamping curricula, and enhancing the overall students' learning experience. The proposed methodology can be used for the analysis of any CPN, and it is illustrated with a network of courses taught at the California Institute of Technology. The network data analyzed in this paper is publicly available in the GitHub repository.

翻译：理解课程间的复杂关系系统对大学的教育使命至关重要。本文致力于研究课程-先修网络（CPN），其中节点表示课程，有向链接表示课程间的正式先修关系。CPN的主要目标是建模课程间的相互作用，展现学术课程体系中的知识流动，并作为可视化、分析和优化复杂课程体系的关键工具。首先，我们考虑几种经典的中心性度量，探讨它们在CPN语境中的含义，并将其用于识别重要课程。其次，我们通过网络拓扑分层描述CPN的层次结构。最后，进行相互依赖分析，该分析能够量化大学各部门间知识流动的强度，并有助于识别最内依赖、最具影响力和跨学科的研究领域。我们探讨了学生、教师和管理人员如何利用课程-先修网络来发现重要课程、改进现有课程并创建新课程、导航复杂课程体系、分配教学资源、增加院系间的跨学科互动、重新设计课程体系以及提升学生的整体学习体验。所提出的方法可适用于任何CPN的分析，并以加州理工学院讲授的课程网络为例进行说明。本文分析的网络数据已公开于GitHub仓库中。