Fundamental patterns of signal propagation in complex networks

Various disasters stem from minor perturbations, such as the spread of infectious diseases and cascading failure in power grids. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have proposed basic propagation patterns for perturbation and explored the impact of basic network motifs on the collective response to these perturbations. However, the current framework is limited in its ability to decouple interactions and, therefore, cannot analyze more complex structures. In this article, we establish an effective, robust, and powerful propagation framework under a general dynamic model. This framework reveals classical and dense network motifs that exert critical acceleration on signal propagation, often reducing orders of magnitude compared with conclusions generated by previous work. Moreover, our framework provides a new approach to understand the fundamental principles of complex systems and the negative feedback mechanism, which is of great significance for researching system controlling and network resilience.