Comparative analysis of course prerequisite networks for five Midwestern public institutions

Abstract

Abstract We present the first formal network analysis of curricular networks for public institutions, focusing around five midwestern universities. As a first such study of public institutions, our analyses are primarily macroscopic in nature, observing patterns in the overall course prerequisite networks (CPNs) and Curriculum Graphs (CGs). An overarching objective is to better understand CPN variability and patterns across different institutions and how these patterns relate to curricular outcomes. In addition to computing well known network centrality measures to capture courses of importance in the CPNs studied, we have also formulated some newer methods with specific relevance to the curricular domains and corresponding graph types at hand. We have discovered that a new graph theoretic measure of node importance which we call reach, based on the well-known concept of reachability, is needed to more accurately express the critical nature of some introductory courses in a university. Another analytical novelty that we introduce and apply to the subject of CPNs is the Longest Paths Induced sub-Graph (LPIG) of the CPN, which yields information on relatively constrained programs and pathways. Finally, we have established a new connection between clustering of the CG and meta-majors at Southern Illinois University Edwardsville (SIUE), providing clusterings of the other public institution CGs as useful heuristics of major groupings as well. This work is borne from collaboration between academic units and academic advising with hopes of practical benefits towards aiding student advising.

Keywords

• Course prerequisite network
• Curriculum graph
• Directed acyclic graph