Food flows underpin the complex food supply chains that are prevalent in our increasingly globalized world. Recently, much effort has been devoted to evaluating the resources (e.g. water, carbon, nutrients) embodied in food trade. Now, research is needed to understand the scientific principles of the food commodity flows that underpin these virtual resource transfers. How do food flows vary with spatial scale? To address this question, we present an empirical analysis of food commodity flow networks across the full spectrum of spatial scales: global, national, and village. We discover properties of both scale invariance and scale dependence in food flow networks. The statistical distribution of node connectivity and mass flux are consistent across scales. Node connectivity follows a generalized exponential distribution, while node mass flux follows a Gamma distribution across scales. Similarly, the relationship between node connectivity and mass flux follows a power law across scales. However, the parameters of the distributions change with spatial scale. Mean node connectivity and mass flux increase with increasing scale. A core group of nodes exists at all scales, but node centrality increases as the spatial scale decreases, indicating that some households are more critical to village food exchanges than countries are to global trade. Remarkably, the structural network properties of food flows are consistent across spatial scales, indicating that a universal mechanism may underpin food exchange systems. In future research, this understanding can be used to develop theoretical models of food flow networks and to model food flows at resolutions for which empirical information is not available.