To slow the spread of the novel coronavirus, many universities shifted to online instruction and now face the question of whether and how to resume in-person instruction. This article uses transcript data from a medium-sized American university to describe three enrollment networks that connect students through classes and in the process create social conditions for the spread of infectious disease: a university-wide network, an undergraduate-only network, and a liberal arts college network. All three networks are 'small worlds' characterized by high clustering, short average path lengths, and multiple independent paths connecting students. Students from different majors cluster together, but gateway courses and distributional requirements create cross-major integration. Connectivity declines when large courses of 100 students or more are removed from the network, as might be the case if some courses are taught online, but moderately sized courses must also be removed before less than half of student-pairs are connected in three steps and less than two-thirds in four steps. In all simulations, most students are connected through multiple independent paths. Hybrid models of instruction can reduce but not eliminate the potential for epidemic spread through the small worlds of course enrollments.

中文翻译：

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大学课程的小世界网络：流行病在大学校园中传播的含义

为了减缓新型冠状病毒的传播，许多大学转向在线教学，现在面临是否以及如何恢复面对面教学的问题。本文使用来自美国中型大学的成绩单数据来描述三个招生网络，这些网络通过课程将学生联系在一起，并在此过程中为传染病的传播创造了社会条件：一个大学范围的网络，一个仅限本科生的网络和一个文理学院网络。所有这三个网络都是“小世界”，其特点是集群高，平均路径长度短，连接学生的多个独立路径。来自不同专业的学生聚集在一起，但是入门课程和分配要求创建了跨专业集成。当从网络上删除100个或更多学生的大型课程时，连接性下降，这可能是某些在线课程在网上授课的情况，但是中等规模的课程也必须被删除，然后通过三步连接少于一半的学生对，在四个步骤中不到三分之二。在所有模拟中，大多数学生是通过多个独立路径连接的。混合教学模式可以减少但不能消除在较小的课程注册人数中流行的可能性。