Sarker Arnab, Northrup Natalie, Jadbabaie Ali
Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02139.
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.
Proc Natl Acad Sci U S A. 2024 Mar 19;121(12):e2315931121. doi: 10.1073/pnas.2315931121. Epub 2024 Mar 12.
Higher-order network models are becoming increasingly relevant for their ability to explicitly capture interactions between three or more entities in a complex system at once. In this paper, we study homophily, the tendency for alike individuals to form connections, as it pertains to higher-order interactions. We find that straightforward extensions of classical homophily measures to interactions of size 3 and larger are often inflated by homophily present in pairwise interactions. This inflation can even hide the presence of anti-homophily in higher-order interactions. Hence, we develop a structural measure of homophily, simplicial homophily, which decouples homophily in pairwise interactions from that of higher-order interactions. The definition applies when the network can be modeled as a simplicial complex, a mathematical abstraction which makes a closure assumption that for any higher-order relationship in the network, all corresponding subsets of that relationship occur in the data. Whereas previous work has used this closure assumption to develop a rich theory in algebraic topology, here we use the assumption to make empirical comparisons between interactions of different sizes. The simplicial homophily measure is validated theoretically using an extension of a stochastic block model for simplicial complexes and empirically in large-scale experiments across 16 datasets. We further find that simplicial homophily can be used to identify when node features are valuable for higher-order link prediction. Ultimately, this highlights a subtlety in studying node features in higher-order networks, as measures defined on groups of size can inherit features described by interactions of size [Formula: see text].
高阶网络模型因其能够一次性明确捕捉复杂系统中三个或更多实体之间的相互作用而变得越来越重要。在本文中，我们研究同质性，即相似个体形成连接的倾向，因为它与高阶相互作用有关。我们发现，将经典同质性度量直接扩展到大小为3及更大的相互作用时，往往会受到成对相互作用中同质性的影响而被夸大。这种夸大甚至可能掩盖高阶相互作用中反同质性的存在。因此，我们开发了一种同质性的结构度量，即单纯形同质性，它将成对相互作用中的同质性与高阶相互作用中的同质性解耦。当网络可以建模为单纯复形时，该定义适用，单纯复形是一种数学抽象，它做出了一个封闭假设，即对于网络中的任何高阶关系，该关系的所有相应子集都出现在数据中。虽然先前的工作已经使用这个封闭假设在代数拓扑中发展了丰富的理论，但在这里我们使用这个假设对不同大小的相互作用进行实证比较。单纯形同质性度量在理论上使用单纯复形的随机块模型扩展进行了验证，并在16个数据集的大规模实验中进行了实证验证。我们进一步发现，单纯形同质性可用于识别节点特征何时对高阶链接预测有价值。最终，这突出了在高阶网络中研究节点特征时的一个微妙之处，因为在大小为的组上定义的度量可以继承由大小为[公式：见正文]的相互作用所描述的特征。
