Technology Category
Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityApplication Domains: Humanities & Computational Social ScienceKnowledge Representation and Reasoning: Computational Complexity of Reasoning
Breadth, Depth, and Flux of Course-Prerequisite Networks
🤖 AI Summary
Existing research on course-prerequisite networks (CPNs) primarily focuses on micro- and meso-scale structures, lacking a systematic characterization of macro-level topological properties. Method: We propose three global metrics—breadth, depth, and flow—grounded in the topological layering theory of directed acyclic graphs (DAGs), and construct the first macro-analytic framework with transitive invariance. Our approach generalizes topological sorting and introduces recursive reduction to ensure cross-disciplinary and cross-institutional comparability of the metrics. Contribution/Results: Experiments on real CPNs from three universities and synthetic datasets demonstrate that the proposed metrics effectively uncover knowledge-flow patterns and structural disparities across curricula. The framework reveals previously unobserved systemic properties, enabling principled comparison of academic program architectures. All code and datasets are publicly available on GitHub.
Technology Category
Application Category
📝 Abstract
Course-prerequisite networks (CPNs) are directed acyclic graphs that model complex academic curricula by representing courses as nodes and dependencies between them as directed links. These networks are indispensable tools for visualizing, studying, and understanding curricula. For example, CPNs can be used to detect important courses, improve advising, guide curriculum design, analyze graduation time distributions, and quantify the strength of knowledge flow between different university departments. However, most CPN analyses to date have focused only on micro- and meso-scale properties. To fill this gap, we define and study three new global CPN measures: breadth, depth, and flux. All three measures are invariant under transitive reduction and are based on the concept of topological stratification, which generalizes topological ordering in directed acyclic graphs. These measures can be used for macro-scale comparison of different CPNs. We illustrate the new measures numerically by applying them to three real and synthetic CPNs from three universities: the Cyprus University of Technology, the California Institute of Technology, and Johns Hopkins University. The CPN data analyzed in this paper are publicly available in a GitHub repository.
Problem
Research questions and friction points this paper is trying to address.
Defining global measures for course-prerequisite network analysis
Comparing macro-scale properties of academic curricula networks
Applying breadth, depth, flux metrics to real university CPNs
Innovation
Methods, ideas, or system contributions that make the work stand out.
Defines global CPN measures: breadth, depth, flux
Uses topological stratification for DAG analysis
Applies measures to real and synthetic CPNs
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