超越成对交互的网络：结构与动力学
Networks beyond pairwise interactions: structure and dynamics
摘要：
许多生物、社会和技术系统的复杂性源于其单元之间丰富的相互作用。在过去的几十年里，大量的复杂系统被成功地描述为网络，其相互作用的节点对通过链路连接。然而，在面对面的人类交流、化学反应和生态系统中，相互作用可以发生在三个或更多节点的群体中，而不能简单地用简单的二元体来描述。直到最近，很少有人关注真正的复杂系统的高阶体系结构。然而，越来越多的证据表明，考虑这些系统的高阶结构可以大大提高我们的建模能力，并帮助我们理解和预测它们的新兴动力学行为。在这里，我们提出了一个完整的概述新兴领域的网络超越成对的相互作用。我们首先讨论的方法来表示高阶的相互作用，并给出一个统一的介绍用于描述高阶系统的不同的框架，突出现有的概念和表示之间的联系。我们回顾的措施，旨在表征这些系统的结构和在文献中提出的模型，以产生合成结构，如随机和不断增长的单纯形复合体，二分图和超图。我们介绍并讨论了迅速增长的研究高阶动力系统和动力拓扑。我们专注于新出现的现象特征里程碑式的动力学过程，如扩散，传播，同步和游戏，当扩展到两两相互作用。我们阐明了高阶拓扑结构和动力学性质之间的关系，并总结了经验应用，提供了一个展望当前的建模和概念前沿。
英文摘要：
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads. Until recently, little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their emerging dynamical behaviors. Here, we present a complete overview of the emerging field of networks beyond pairwise interactions. We first discuss the methods to represent higher-order interactions and give a unified presentation of the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed in the literature to generate synthetic structures, such as random and growing simplicial complexes, bipartite graphs and hypergraphs. We introduce and discuss the rapidly growing research on higher-order dynamical systems and on dynamical topology. We focus on novel emergent phenomena characterizing landmark dynamical processes, such as diffusion, spreading, synchronization and games, when extended beyond pairwise interactions. We elucidate the relations between higher-order topology and dynamical properties, and conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers.
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