Homophily is the seemingly ubiquitous tendency for people to connect with similar others, which is fundamental to how society organizes. Even though many social interactions occur in groups, homophily has traditionally been measured from collections of pairwise interactions involving just two individuals. Here, we develop a framework using hypergraphs to quantify homophily from multiway, group interactions. This framework reveals that many homophilous group preferences are impossible; for instance, men and women cannot simultaneously exhibit preferences for groups where their gender is the majority. This is not a human behavior but rather a combinatorial impossibility of hypergraphs. At the same time, our framework reveals relaxed notions of group homophily that appear in numerous contexts. For example, in order for US members of congress to exhibit high preferences for co-sponsoring bills with their own political party, there must also exist a substantial number of individuals from each party that are willing to co-sponsor bills even when their party is in the minority. Our framework also reveals how gender distribution in group pictures varies with group size, a fact that is overlooked when applying graph-based measures.

中文翻译：

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高阶同质性不可能组合

同性恋是人们与他人相处的一种普遍存在的趋势，这是社会组织方式的基础。即使许多社会互动是在群体中发生的，传统上也从仅涉及两个人的成对互动的集合中测量同伦。在这里，我们开发了一个使用超图的框架，用于从多路，群体互动中量​​化同构。这个框架表明，许多同质的团体偏好是不可能的。例如，男人和女人不能同时表现出对性别占多数的群体的偏爱。这不是人类的行为，而是超图的组合不可能。同时，我们的框架揭示了在许多情况下出现的同质群的轻松概念。例如，为了使美国国会议员对与自己的政党共同发起法案具有较高的偏好，即使当政党属于少数派时，也必须有来自每个政党的大量个人愿意共同发起法案。我们的框架还揭示了组图片中的性别分布如何随组大小而变化，这一事实在应用基于图的度量时会被忽略。