Transformability of dynamics on higher-order networks

Complex systems often involve interactions within groups, namely higher-order networks, rather than simple pairwise connections, which fundamentally reshape how collective dynamics unfold. However, it remains poorly understood how dynamics transform across different network structures, limiting our ability to predict and guide collective dynamical behaviors. Here, we propose a holistic framework that bridges the relationship between dynamics in pairwise and higher-order systems, showing that these processes follow systematic transformations. Focusing on contagion dynamics, we identify and quantify the dynamical and structural factors that explain transformability and discuss guiding criteria for it, revealing an integrated model governed by these factors from the perspective of system disorder. We further demonstrate that these insights apply to opinion dynamics, highlighting the broad relevance of our model. Our results advance understanding of dynamic transformability and provide a foundation for influencing behaviors in real-world networked intelligent higher-order systems. Complex systems often interact through groups rather than simple pairwise connections, which can reshape how dynamics unfold on networks. Here, the authors develop a framework based on system disorder to quantify how dynamics transform across higher-order structures, uncover structural and dynamical governing factors, and demonstrate its applicability across contagion and opinion processes.