Signal propagation in complex networks drives epidemics, is responsible for information going viral, promotes trust and facilitates moral behavior in social groups, enables the development of misinformation detection algorithms, and it is the main pillar supporting the fascinating cognitive abilities of the brain, to name just some examples. The geometry of signal propagation is determined as much by the network topology as it is by the diverse forms of nonlinear interactions that may take place between the nodes. Advances are therefore often system dependent and have limited translational potential across domains. Given over two decades worth of research on the subject, the time is thus certainly ripe, indeed the need is urgent, for a comprehensive review of signal propagation in complex networks. We here first survey different models that determine the nature of interactions between the nodes, including epidemic models, Kuramoto models, diffusion models, cascading failure models, and models describing neuronal dynamics. Secondly, we cover different types of complex networks and their topologies, including temporal networks, multilayer networks, and neural networks. Next, we cover network time series analysis techniques that make use of signal propagation, including network correlation analysis, information transfer and nonlinear correlation tools, network reconstruction, source localization and link prediction, as well as approaches based on artificial intelligence. Lastly, we review applications in epidemiology, social dynamics, neuroscience, engineering, and robotics. Taken together, we thus provide the reader with an up-to-date review of the complexities associated with the network’s role in propagating signals in the hope of better harnessing this to devise innovative applications across engineering, the social and natural sciences as well as to inspire future research.

复杂网络中的信号传播驱动流行病，负责信息病毒式传播，促进信任并促进社会群体的道德行为，促进错误信息检测算法的发展，它是支持大脑迷人认知能力的主要支柱，以命名只是一些例子。信号传播的几何形状既取决于网络拓扑结构，也取决于节点之间可能发生的各种形式的非线性相互作用。因此，进步通常取决于系统，并且跨领域的转化潜力有限。鉴于对该主题进行了 20 多年的研究，因此对复杂网络中的信号传播进行全面审查的时机肯定已经成熟，而且确实迫切需要。我们在这里首先调查确定节点之间交互性质的不同模型，包括流行病模型、Kuramoto 模型、扩散模型、级联故障模型和描述神经元动力学的模型。其次，我们涵盖了不同类型的复杂网络及其拓扑结构，包括时间网络、多层网络和神经网络。接下来，我们将介绍利用信号传播的网络时间序列分析技术，包括网络相关分析、信息传输和非线性相关工具、网络重构、源定位和链路预测，以及基于人工智能的方法。最后，我们回顾了流行病学、社会动力学、神经科学、工程学和机器人学中的应用。综合起来，