Breadth, Depth, and Flux of Course-Prerequisite Networks

TL;DR

This paper introduces three new global measures—breadth, depth, and flux—for analyzing course-prerequisite networks, providing macro-scale insights into curricula structure beyond traditional micro- and meso-scale analyses.

Contribution

The paper defines and studies three novel global measures for course-prerequisite networks, based on topological stratification, enabling macro-scale comparisons of curricula.

Findings

Applied measures to real and synthetic CPNs from three universities.

Demonstrated invariance of measures under transitive reduction.

Provided publicly available CPN data for further research.

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.