To limit the spread of the novel coronavirus on college campuses, a common strategy for the Fall 2020 and Spring 2021 terms has been to offer instruction weighted toward hybrid or fully online modalities. Colleges are now considering whether and how to expand hybrid or fully in-person instruction for future terms, and learn lessons from this experience for future use. Our paper uses Fall 2019 enrollment data for a medium-sized public American university to analyze whether some student groupings by class standing or course level are more susceptible to the spread of infectious disease through academic enrollment networks. Replicating Weeden and Cornwell [8], we find that enrollment networks at the institution are "small worlds" characterized by high clustering, short average path lengths, and multiple independent connections. Connectivity decreases as class standing (graduate vs. undergraduate; senior vs. freshman) and course level increase; as students move from generalized to specialized course loads, networks cluster by major. Holding other factors constant, policies focusing on in-person instruction for lower division students conflict with the greater risk of infectious spread through a lower division network in the absence of additional steps to minimize academic connectivity. There are academic and financial incentives for emphasizing the freshman experience, including concerns about student attrition from the first to second academic year and recouping costs of infrastructure investments in dormitories. Possible solutions could include (i) restricting face-to-face or hybrid instruction to courses in students' academic majors, which would disrupt larger networks into smaller ones and thus restrict the spread of infection across majors, and (ii) take a "scalpel" approach to instruction modes by moving online courses most likely to facilitate epidemic spread.