Revisiting the small-world property of co-enrollment networks: A network analysis of hybrid course delivery strategies
Authors: Wu Di , Hamilton Hanna , Jagrowski Liam , Nazzal Dima , Steimle Lauren 
Published: December 2022

Infectious disease outbreaks bring new challenges to campus operations at institutions of higher education (IHEs). At the beginning of the COVID-19 pandemic, as a precaution against COVID-19 transmission on their campuses, many IHEs shifted to entirely remote courses in the Spring 2020 semester. As these institutions prepared for the Fall 2020 semester, their administrations evaluated the extent to which remote courses should continue. While remote courses may reduce the number of students who interact on campus and thus mitigate the risk of disease spread, there may be academic and financial downsides. Methodology: With de-identified enrollment, course schedule, and student profile data from the Fall 2019 semester at Georgia Institute of Technology (Georgia Tech), we construct a co-enrollment network, which is a representation of student connections through courses. In this co-enrollment network, we observe the small-world property in which the average path length among reachable student pairs is short and nearly all students are connected to each other in the main component of the network through multiple independent paths. We also see high connectivity between different majors. Then, we apply various hybrid instructional mode strategies to this co-enrollment network and use network connectivity and in-person instruction metrics to compare these strategies from both health and academic perspectives, by their impacts on various groups of students, and based on the trade-off between network connectivity and in-person instruction. Results: Although these strategies result in decreased network connectivity, they do not remove the small-world property. When comparing the strategies in terms of network connectivity, we find three different strategy types to be the most favorable. Even under these strategies, the percentage of students with in-person courses that could be exposed rises quickly with initial infection rates. When comparing the strategies in terms of in-person instruction, the most favorable strategies select a fixed percentage of courses for each subject to be delivered remotely. We then consider the impacts of these strategies on various groups of students to evaluate if there may be disparate impacts across these groups. In general, we find that strategies with more remote courses result in less disparate impacts on network connectivity and in-person instruction across these groups. In addition, we generally see less in-person instruction for lower-level students (i.e. first-year students and sophomores) compared to upper-level students. Regarding the trade-off between network connectivity and in-person instruction, the only strategy that is suboptimal under all scenarios in this study is the 1000s and 4000s only strategy, which keeps all 1000- and 4000-level courses in-person. This is because of its large quantity of remote courses, the large 1000- and 4000-level courses, the highly central 1000-level courses, and the high connectivity among first-year students and seniors. Importance: By quantitatively comparing network connectivity and in-person instruction for these various strategies, campus administrators can weigh the physical health, academic performance, and mental health of students, along with the financial well-being of their academic institution when responding to infectious disease outbreaks.