SIAM Review, Volume 65, Issue 3, Page 686-731, August 2023.
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity of graphs: A graph consists of nothing more than a set of vertices and a set of edges, describing relationships between pairs of such vertices. This simple combinatorial structure makes graphs interpretable and flexible modeling tools. The simplicity of graphs as system models, however, has been scrutinized in the literature recently. Specifically, it has been argued from a variety of different angles that there is a need for higher-order networks, which go beyond the paradigm of modeling pairwise relationships, as encapsulated by graphs. In this survey article we take stock of these recent developments. Our goals are to clarify (i) what higher-order networks are, (ii) why these are interesting objects of study, and (iii) how they can be used in applications.

中文翻译：

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什么是高阶网络？

《SIAM 评论》，第 65 卷，第 3 期，第 686-731 页，2023 年 8 月。
使用图形语言对复杂系统和数据进行基于网络的建模已成为一系列不同学科的重要主题。可以说，这种基于图的视角的成功源于图的相对简单性：图仅由一组顶点和一组边组成，描述了这些顶点对之间的关​​系。这种简单的组合结构使图形成为可解释的和灵活的建模工具。然而，图作为系统模型的简单性最近在文献中得到了仔细研究。具体来说，人们从各种不同的角度认为需要高阶网络，这超出了图形封装的成对关系建模范式。在这篇调查文章中，我们盘点了这些最新进展。