Group interactions occur frequently in social settings, yet their properties beyond pairwise relationships in network models remain unexplored. In this work, we study homophily, the nearly ubiquitous phenomena wherein similar individuals are more likely than random to form connections with one another, and define it on simplicial complexes, a generalization of network models that goes beyond dyadic interactions. While some group homophily definitions have been proposed in the literature, we provide theoretical and empirical evidence that prior definitions mostly inherit properties of homophily in pairwise interactions rather than capture the homophily of group dynamics. Hence, we propose a new measure, $k$-simplicial homophily, which properly identifies homophily in group dynamics. Across 16 empirical networks, $k$-simplicial homophily provides information uncorrelated with homophily measures on pairwise interactions. Moreover, we show the empirical value of $k$-simplicial homophily in identifying when metadata on nodes is useful for predicting group interactions, whereas previous measures are uninformative.
翻译:在社会环境中经常出现群体互动,但在网络模型中,他们超越对称关系特性的属性仍未被探索。在这项工作中,我们研究几乎无处不在的现象,即近似个体更有可能与随机形成相互联系,并在简单复杂的情况下界定,将网络模型的概括化,超越了dyatic互动。虽然文献中提出了某些群体同义定义,但我们提供了理论和经验证据,证明先前的定义主要继承了对称互动中同质特性,而不是群体动态中同质的特性。因此,我们提出了一个新的尺度,即$k$-simplical同质,在群体动态中恰当地识别同质。在16个经验网络中,$k-simplical同质提供了与对称互动的同质措施无关的信息。此外,我们在确定节点元元对于预测群体互动有用时,我们展示了美元-简易同质的经验价值,而以前的措施则是非强制性的。