What Are Higher-Order Networks?

IF 10.8 1区 数学 Q1 MATHEMATICS, APPLIED
SIAM Review Pub Date : 2023-08-08 DOI:10.1137/21m1414024
Christian Bick, Elizabeth Gross, Heather A. Harrington, Michael T. Schaub
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引用次数: 0

Abstract

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.
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:图只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具有可解释性和灵活的建模工具。然而,图作为系统模型的简单性在最近的文献中受到了仔细的审查。具体来说,有人从各种不同的角度认为,需要更高阶的网络,它超越了用图封装的成对关系建模的范式。在这篇调查文章中,我们对这些最新进展进行了评估。我们的目标是澄清(i)什么是高阶网络,(ii)为什么这些是有趣的研究对象,以及(iii)如何在应用中使用它们。
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来源期刊
SIAM Review
SIAM Review 数学-应用数学
CiteScore
16.90
自引率
0.00%
发文量
50
期刊介绍: Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.
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