Understanding species' interactions and the robustness of interaction networks to species loss is essential to understand the effects of species' declines and extinctions. In most studies, different types of networks (such as food webs, parasitoid webs, seed dispersal networks, and pollination networks) have been studied separately. We sampled such multiple networks simultaneously in an agroecosystem. We show that the networks varied in their robustness; networks including pollinators appeared to be particularly fragile. We show that, overall, networks did not strongly covary in their robustness, which suggests that ecological restoration (for example, through agri-environment schemes) benefitting one functional group will not inevitably benefit others. Some individual plant species were disproportionately well linked to many other species. This type of information can be used in restoration management, because it identifies the plant taxa that can potentially lead to disproportionate gains in biodiversity.