One of the basic structural reasons that complex networks are "complex" is that they contain an abundant number of (long and short) cycles.Cycles lead to feedbacks and complex dynamical processes.The task of identifying the nodes that are most important for feedback interactions is closely related to the concept of minimum feedback vertex set (FVS).In this presentation I introduce a spin-glass approach to the minimum FVS problem and offer a highly efficient algorithm for solving it[1].As an important application,I show that this algorithm also solves the optimal network attack problem perfectly[2].Our theory and algorithm shall be useful for understanding and improving network resilience.