Two types of interventions are commonly implemented in networks: characteristic intervention, which influences individuals' intrinsic incentives, and structural intervention, which targets the social links among individuals. In this paper we provide a general framework to evaluate the distinct equilibrium effects of both types of interventions. We identify a hidden equivalence between a structural intervention and an endogenously determined characteristic intervention. Compared with existing approaches in the literature, the perspective from such an equivalence provides several advantages in the analysis of interventions that target network structure. We present a wide range of applications of our theory, including identifying the most wanted criminal(s) in delinquent networks and targeting the key connector for isolated communities.