Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a consistent picture of a higher-order dataset’s structure. In contrast, the connection patterns of individuals or entities in empirical systems are often stratified by interaction size. Ignoring this fact can aggregate connection patterns that exist only at certain scales of interaction. To isolate these scale-dependent patterns, we present an approach for analyzing higher-order datasets by filtering interactions by their size. We apply this framework to several empirical datasets from three domains to demonstrate that data practitioners can gain valuable information from this approach.

中文翻译：

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过滤高阶数据集

许多复杂的系统通常包含两个以上节点之间的交互，称为高阶相互作用，这可以显着改变这些系统的结构。研究人员通常假设所有交互都描绘了高阶数据集结构的一致图景。相反，经验系统中个体或实体的连接模式通常按交互大小进行分层。忽略这一事实可能会聚合仅存在于特定交互规模的连接模式。为了隔离这些依赖于尺度的模式，我们提出了一种通过按大小过滤交互来分析高阶数据集的方法。我们将该框架应用于来自三个领域的几个经验数据集，以证明数据从业者可以从这种方法中获得有价值的信息。