Material flows—such as food trade—allow human societies to rely on natural resources available both locally and in other regions of the planet. Thus, in a globalized world, multiple pools of the same resource are often harvested by multiple users through a network of interactions. It is not clear to what extent the interconnectedness, structure and modularity (that is, when subsystems of nodes exhibit stronger internal connectivity) of such a network may affect the resilience of the system. Here, we develop a theoretical framework to investigate the impact of globalization on the sustainable use of natural resources for food production. We find that the resilience of the system may either increase or decrease with the network’s interconnectedness and modularity, depending on the network structure. Global food trade exhibits a heterogeneous structure and its resilience is decreasing with the increase in connectivity of the past few decades.