Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and measuring dynamic networks featuring higher-order relations. At the same time, while network analysis has been more widely adopted to investigate the structure and evolution of law as a complex system, the utility of dynamic higher-order networks in the legal domain has remained largely unexplored. Setting out to change this, we introduce temporal hypergraphs as a powerful tool for studying legal network data. Temporal hypergraphs generalize static graphs by (i) allowing any number of nodes to participate in an edge and (ii) permitting nodes or edges to be added, modified or deleted. We describe models and methods to explore legal hypergraphs that evolve over time and elucidate their benefits through case studies on legal citation and collaboration networks that change over a period of more than 70 years. Our work demonstrates the potential of dynamic higher-order networks for studying complex legal systems, and it facilitates further advances in legal network analysis.

This article is part of the theme issue ‘A complexity science approach to law and governance’.

复杂性科学为理解物理、生物和社会系统提供了强大的框架，而网络分析是其主要工具之一。由于许多复杂系统表现出随时间变化的多边相互作用，近年来，网络科学家对建模和测量具有高阶关系的动态网络越来越感兴趣。与此同时，虽然网络分析已被更广泛地用于研究法律作为一个复杂系统的结构和演化，但动态高阶网络在法律领域的效用在很大程度上仍未得到探索。为了改变这一点，我们引入了时间超图作为研究法律网络数据的强大工具。时间超图通过 (i) 允许任意数量的节点参与边以及 (ii) 允许添加、修改或删除节点或边来概括静态图。我们描述了探索随时间演变的法律超图的模型和方法，并通过对 70 多年变化的法律引用和协作网络的案例研究来阐明其好处。我们的工作展示了动态高阶网络在研究复杂法律系统方面的潜力，并促进了法律网络分析的进一步发展。

本文是主题“法律和治理的复杂性科学方法”的一部分。