A new paper by sociologists Kim Weeden and Benjamin Cornwell, from the Department of Sociology and the Center for the Study of Inequality, shows just how interconnected students are on a college campus, with implications for whether universities should resume in-person instruction until the covid-19 epidemic is better controlled.
In their paper, recently released in Sociological Science, Weeden and Cornwell use transcript data from Cornell to map the structure of enrollment networks that connect students to each other through their courses. These course enrollment networks are classic “small worlds” networks, with high levels of clustering and short distances connecting any randomly chosen pair of students.
Over a typical week, the average student – graduate or undergraduate -- will be enrolled in courses with 529 different students,” says Weeden. “But, this is just an average. Graduate students are co-enrolled with fewer other students. Among undergraduates, however, co-enrollment jumps to more than 600 students. It’s even higher for first and second-year undergraduates, who are more likely to take large, introductory courses.”
Although only 2.4% of all student pairs enroll in the same course together, 59% can “reach” each other in two steps – or two “elbow bumps” – meaning both students take a class with the same third student. After three steps, 92% of student pairs are connected, and after four steps, 97% are connected. The longest distance in the network is 10 steps. As Weeden says, “In some ways it is more remarkable that a 3rd year Law student can ‘reach’ a first-year student in Fiber Science and Apparel Design at all than that it may take up to 10 elbow bumps to get there.”
Weeden and Cornwell also show that connections between students typically involve multiple different pathways. It’s not just that Student A and Student B are connected because they both share a course with Student C. They may also share a course with Students D, E, and F. This makes it more difficult to think about how to reduce connectivity: it’s not just one course, or one set of students, that are creating the small world.
Figure 1. University Enrollment Network
Note: Light gray squares represent courses, and larger gray squares with red borders indicate courses with ≥ 100 students enrolled. Students are represented by small circles with colors identifying their major(s): yellow = humanities, arts, and design; dark blue = social sciences; orange = STEM; red = multidisciplinary/mixed; green= undeclared; light blue = business and law. Students’ enrollment in particular courses is indicated with light gray lines. This diagram excludes 338 nodes that were not connected to this main component.
Students from different majors tend to be clustered together (see Figure 1), reflecting the common courses they take for their majors. However, distribution requirements and interest-based exploration create connections across majors. A classic Cornell example is HADM 4300: Introduction to Wines, which enrolls more than 700 students and is popular with students from across campus.
Weeden and Cornwell also examined how the structure of enrollment networks change if large courses are taught online and smaller courses are taught through face-to-face instruction. They found that removing courses with 100 or more students elongates indirect chains of contact, but still leaves 77% of student pairs connected after 3 steps. When they reduced the cap to 30 students, only 21% of student pairs are connected in 3 steps or less, and more students are found outside the main component of the network – the ball of spaghetti in Figure 1 – but more than half are still connected in 5 steps.
The course enrollment network for undergraduates and for students in the liberal arts college are, if anything, more tightly connected than the university-wide network. In these networks, 99% of students are connected by 3 elbow bumps. As in the university network, hybrid models of instruction reduce connectivity among undergraduates, but still leave fairly short path lengths and multiple pathways connecting students.
The irony, says Weeden, is that the features of universities that make them such vibrant intellectual and social environments also make them fertile social conditions for the epidemic spread of a virus. And, she says, “We just considered connections through classes. Students are also connected to each other, and to faculty and staff, through their residences, extracurricular activities, athletics, parties, and even by sharing the same physical space as they travel to and from classes.” Even with widespread testing, she says, it’s a daunting challenge to safely bring students, faculty, and staff back to campus.
Weeden and Cornwell’s paper has already received quite a bit of attention in the national press, with coverage in The Chronicle for Higher Education, Inside Higher Education, Forbes, the Wall Street Journal, and NPR. It’s also been covered in the Daily Sun.