标题： 多路复用体：多路复用网络的极限 显示英文标题

标题： Multiplexons: Limits of Multiplex Networks

摘要： 在多层网络中，一组节点通过不同类型的交互连接，每种交互都被表示为网络中的一个单独图层。 多层网络已成为建模大规模复杂系统的关键工具，这是由于社会、工业和生物领域中多种交互的广泛共存。 这促使了研究大规模多层网络性质的严格且易于应用的框架的发展。 在本文中，我们提供了密集多层网络极限理论的自包含介绍，类似于图核理论（密集图的极限理论）。 作为应用，我们推导了常用的多层特征的极限对应物，例如度分布和聚类系数。 我们还提供了一系列说明性例子，包括Erdős-Rényi和非均匀随机图模型的相关版本以及动态网络。 最后，我们讨论了多层网络如何融入装饰图的更广泛框架，以及如何从装饰图的极限理论中恢复收敛结果。 文章最后概述了进一步发展多层极限理论的几个未来方向。 显示英文摘要

摘要： In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to the widespread coexistence of diverse interactions in social, industrial, and biological domains. This motivates the development of a rigorous and readily applicable framework for studying properties of large multiplex networks. In this article, we provide a self-contained introduction to the limit theory of dense multiplex networks, analogous to the theory of graphons (limit theory of dense graphs). As applications, we derive limiting analogues of commonly used multiplex features, such as degree distributions and clustering coefficients. We also present a range of illustrative examples, including correlated versions of Erd\H{o}s-R\'enyi and inhomogeneous random graph models and dynamic networks. Finally, we discuss how multiplex networks fit within the broader framework of decorated graphs, and how the convergence results can be recovered from the limit theory of decorated graphs. Several future directions are outlined for further developing the multiplex limit theory.