The idea of “six degrees of separation” is widely understood to suggest that a small number of indirect social connections link any two people.

On a college campus, the reality among students is more like three degrees of separation, according to an analysis of course enrollments at Cornell by sociologists in the College of Arts and Sciences.

Their findings reveal how quickly COVID-19 could spread through “small-world” campus networks if no precautions were taken, knowledge that is helping colleges and universities across the country evaluate whether in-person instruction can resume safely this fall amid the pandemic.

“You have a very large community that is closely interconnected through short transmission chains,” said Ben Cornwell, associate professor of sociology. “It’s a very delicate combination.”

Cornwell and Kim Weeden, the Jan Rock Zubrow ’77 Professor of the Social Sciences, are the authors of “The Small-World Network of College Classes: Implications for Epidemic Spread on a University Campus,” published May 27 in Sociological Science.

The scholars analyzed fall 2019 course enrollment data for more than 22,000 Cornell students, including roughly 14,800 undergraduates and a subset of those enrolled in the College of Arts and Sciences.

The average student, they found, encountered up to 529 other students during a week of classes, assuming full attendance. First- or second-year undergraduates saw more students, graduate students less.

Overall, the chance that any possible pair of students shared a class together, meaning they were connected to each other in one step, was less than 3%. But adding a second step – an indirect link to a third student through another class – connected 59% of all students, and nearly 90% of undergraduates. By three steps, courses linked 92% of all possible pairs of Cornell students and virtually all undergraduates.

“There’s a lot of clustering, there’s a lot of connectivity between the students,” Weeden said. “Even students who aren’t in the same class together are connected indirectly by very few steps.”

The degree of interconnectedness was a surprise, the researchers said.

Such a close-knit campus network does not mean a COVID-19 outbreak would occur, Weeden and Cornwell said, stressing that they are not epidemiologists. It does, however, create more fertile conditions for a potential epidemic spread of the virus than other network structures would, like if students in different majors or colleges never interacted with each other.

“This is a small world that needs to be handled very carefully,” Cornwell said.

To prevent or minimize an outbreak if students return this fall, Cornell and other institutions are considering numerous strategies: moving some classes online; extensive testing; requiring masks and social distancing; and modifying classroom, living and dining spaces.

The research makes clear that just moving large classes online wouldn’t solve the small-world network challenge. Doing so for courses with 100 or more students reduced to 78% the pairs of students reachable in three or fewer steps. A more meaningful drop, to 21%, occurred if classes with 30 or more students transitioned online.

Those thresholds raise questions about whether mitigations to ensure public safety threaten to diminish the quality of the educational experience, the scholars said.

“There’s a reason why colleges and universities are such vibrant intellectual and social spaces to be, and that’s partly because of those connections that you’re creating between students,” Weeden said. “Once you start breaking apart the network to reduce the potential for the transmission of disease, you’re also getting rid of a lot of those positive aspects of a network of students on campus.”

The study, which received a rapid response grant from the Cornell Center for Social Sciences, has opened a dialogue with schools performing similar course enrollment analyses, the researchers said. So far, they said, the basic network patterns look eerily similar whether at a small liberal arts college, Cornell or a state university of 30,000 students.

Weeden and Cornwell applauded Cornell for quickly providing recent enrollment data and weighing its implications for the fall.

“We want to see this work, but we also want to keep an eye on the network structure and make sure it is not putting us at risk,” Cornwell said. “Doing this analysis takes us in that direction and lets us go into this with our eyes open.”