Perturbations in networked dynamical complex systems could cause cascading failures, consequently instability, and eventually collapse of the systems. In this work, we derive a set of formulations that help us understand the mechanism of high-dimensional interactions among components and uncover the principles that control the dynamics of interacting components. Our formulation reduces the system’s high dimensional dynamics to a parsimonious resilience function of a parameter that solely depends on the topology but effectively captures the complex interaction structure. The experimental results demonstrate that the formulation can accurately predict the resilience loss brought about by perturbations and identify the tipping point where the systemic collapse occurs. These predictive results can be used for enhancing a complex system’s ability to withstand perturbations and avert catastrophic collapses. The study highlights the topological properties that can be used as principles for improving the resilience of ecosystems, biological systems, economic systems and technological infrastructures.