Spreading Dynamics on Higher-Order Networks: A Structure-Mechanism-Behavior Perspective with Applications

Spreading in real-world networks, including modern communication and networked systems, often unfolds through group interactions rather than isolated pairwise contacts. Higher-order network representations such as simplicial complexes, hypergraphs, and their temporal, multilayer, and directed extensions provide a principled way to encode group interactions. Unfortunately, existing studies on spreading over these substrates remain fragmented and largely model-centric, offering limited insight into how higher-order representations and contagion mechanisms jointly shape emergent dynamics. This review addresses this gap by introducing a structure-mechanism-behavior three-level perspective that provides a systematic mapping from higher-order network structures and spreading mechanisms to collective behaviors. Within this framework, we compare how different higher-order network representations encode group interactions, introduce a taxonomy of contagion mechanisms, and analyze their structural carrying capacity, defined as the ability of a given representation to support specific contagion mechanisms and the associated dynamical behaviors. We further map specific structure-mechanism combinations to three hallmark emergent behaviors, thereby offering a unified cross-level perspective beyond existing model-centric surveys. These insights are particularly relevant for communication systems involving group interactions, such as social information spreading, cooperative protocols, and distributed networked processes. Lastly, leveraging this three-level perspective, we offer a roadmap for guiding and controlling dynamics on higher-order networks, while discussing future directions in representation choice, mechanism design, and data-driven inference.