A major quest in network and community ecology has been centered on understanding the importance of structural patterns in species interaction networks—the synthesis of who interacts with whom in a given location and time. In the past decades, much effort has been devoted to infer the importance of a particular structure by its capacity to tolerate an external perturbation on its structure or dynamics. Here, we demonstrate that such a perspective leads to inconsistent conclusions. That is, the importance of a network structure changes as a function of the external perturbations acting on a community at any given point in time. Thus, we discuss a research agenda to investigate the relative importance of the structure of ecological networks under an environment‐dependent framework. We hypothesize that only by studying systematically the link between network structure and community dynamics under an environment‐dependent framework, we can uncover the limits at which communities can tolerate environmental changes.