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As colleges grapple with the question of whether and when it will be safe to resume in-person instruction, a newly published working paper analyzing course enrollment patterns at Cornell University found that nearly all students are connected via a shared classmate.

“Over a typical week, the average student will share classes with more than 500 different students,” one of the paper’s authors, Kim Weeden, said in a summary of the results on Twitter. “This number is higher for lower-division students, because they tend to take more large introductory courses. The average student can ‘reach’ only about 4 percent of other students by virtue of sharing a course together, but 87 percent of students can reach each other in two steps, via a shared classmate. By three steps, it’s 98 percent.”

Weeden and Benjamin Cornwell, both sociology professors at Cornell University, also found that a hybrid model in which large courses would be taught online and smaller ones would be taught via face-to-face instruction “would not appreciably reduce the interconnectedness of students in the full course enrollment network.” They found that even after eliminating the 126 classes that had 100 or more students from the analysis, "the campus-wide network remains highly connected."

"These results suggest caution in reopening colleges and universities for face-to-face instruction in response to the COVID-19 pandemic," Weeden and Cornwell wrote in their working paper.

"We were sort of hoping that once you eliminated the 100 biggest courses on campus you might be able to able to disconnect this network: it didn’t work out that way," Weeden, the Jan Rock Zubrow ’77 Professor of the Social Sciences​ at Cornell, said in an interview.

"I think we were a little bit surprised about how tight the connections really are, what a small world it really is, and in particular that there are so many different paths between any two students. It's not just one student who is connecting any given pair of students. It's multiple ways that you can get to student A or student B. Even if they’re not taking a class together, they're likely taking it with a third person that they share in common. One of the lessons is that university administrators may need to think creatively about what’s going on in their local context. Our study was just Cornell, and all universities, even those of fairly similar size, are structured a little bit differently."

"How do we minimize the risk, recognizing first of all that courses are just one way that college students come in contact with each other, particularly on a residential campus?" Weeden said of questions faced by college administrators. "Are there alternative ways we can deliver high-quality content that isn't the standard face-to-face model but isn’t moving everything online, either? Could we put some classes online? Could we think about a block schedule where students take one course for three weeks at a time with the same students and move to another class after that? Are there ways that we can think about structuring some of our classes and still get some of the benefits of face-to-face instruction?"

The working paper, which is based on an analysis of spring 2015 undergraduate course enrollments at Cornell, has not yet been peer reviewed, though Weeden said she and Cornwell feel confident enough in the data and findings to post the paper on an open-science platform. She said as well that the network analysis methodology used in the study is fairly straightforward.

In their working paper, Weeden and Cornwell note limitations of the study, including the fact that the data are reflective of just one university and that "course enrollment networks do not capture the many ways that students are connected outside of the classroom through advisors, friends, parties, athletics and other extra-curricular activities, or living situations."

“At the same time, course enrollment networks may overstate the density of the networks through which a virus is likely to be transmitted,” Weeden and Cornwell wrote. “Most obviously, two students who are co-enrolled in a large lecture course may never come in close physical proximity to each other. Similarly, classes, particularly large ones, rarely achieve full attendance. Future work should consider factors such as physical space within a classroom or attendance rates to fine-tune estimates of how course enrollment networks may pattern the diffusion of a virus, a rumor, an idea, or anything else that can be transmitted through direct or indirect social contact on a college campus.”

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