Connectivity is an important key performance indicator and a focal point of research in large-scale wireless networks. Due to path-loss attenuation of electromagnetic waves, direct wireless connectivity is limited to proximate devices. Nevertheless, connectivity among distant devices can still be attained through a sequence of consecutive multi-hop communication links, which enables routing and disseminating legitimate information across wireless ad hoc networks. Multi-hop connectivity is also foundational for data aggregation in the Internet of things (IoT) and cyberphysical systems (CPS). On the downside, multi-hop wireless transmissions increase susceptibility to eavesdropping and enable malicious network attacks. Hence, security-aware network connectivity is required to maintain communication privacy, detect and isolate malicious devices, and thwart the spreading of illegitimate traffic (e.g., viruses, worms, falsified data, illegitimate control, etc.). In 5G and beyond networks, an intricate balance between connectivity, privacy, and security is a necessity due to the proliferating IoT and CPS, which are featured with massive number of wireless devices that can directly communicate together (e.g., device-to-device, machine-to-machine, and vehicle-to-vehicle communication). In this regards, graph theory represents a foundational mathematical tool to model the network physical topology. In particular, random geometric graphs (RGGs) capture the inherently random locations and wireless interconnections among the spatially distributed devices. Percolation theory is then utilized to characterize and control distant multi-hop connectivity on network graphs. Recently, percolation theory over RGGs has been widely utilized to study connectivity, privacy, and security of several types of wireless networks. The impact and utilization of percolation theory are expected to further increase in the IoT/CPS era, which motivates this tutorial. Towards this end, we first introduce the preliminaries of graph and percolation theories in the context of wireless networks. Next, we overview and explain their application to various types of wireless networks.

中文翻译：

---

渗透理论在大规模无线网络中的应用教程兼调查

连接性是大规模无线网络的重要关键性能指标，也是研究的焦点。由于电磁波的路径损耗衰减，直接无线连接仅限于附近的设备。尽管如此，远程设备之间的连接仍然可以通过一系列连续的多跳通信链路来实现，这使得能够在无线自组织网络中路由和传播合法信息。多跳连接也是物联网 (IoT) 和网络物理系统 (CPS) 中数据聚合的基础。不利的一面是，多跳无线传输增加了窃听的可能性并导致恶意网络攻击。因此，需要具有安全意识的网络连接来维护通信隐私、检测和隔离恶意设备并阻止非法流量（例如病毒、蠕虫、伪造数据、非法控制等）的传播。在 5G 及其他网络中，由于物联网和 CPS 的激增，连接、隐私和安全之间的复杂平衡是必要的，其特点是大量可以直接在一起通信的无线设备（例如，设备到设备、机器对机器和车辆对车辆通信）。在这方面，图论代表了对网络物理拓扑进行建模的基本数学工具。特别是，随机几何图（RGG）捕获空间分布设备之间固有的随机位置和无线互连。然后利用渗流理论来表征和控制网络图上的远程多跳连接。最近，RGG 的渗透理论已被广泛用于研究多种类型无线网络的连接性、隐私性和安全性。渗透理论的影响和利用预计将在 IoT/CPS 时代进一步增加，这也是本教程的动机。为此，我们首先介绍无线网络背景下的图和渗流理论的基础知识。接下来，我们概述并解释它们在各种类型的无线网络中的应用。