Anatomical connectivity can constrain both a neural circuit's function and its underlying computation. This principle has been demonstrated for many small, defined neural circuits. For example, connectome reconstructions have informed models for direction selectivity in the vertebrate retina1,2 as well as the Drosophila visual system.3 In these cases, the circuit in question is relatively compact, well-defined, and has known functions. However, how the connectome constrains global properties of large-scale networks, across multiple brain regions or the entire brain, is incompletely understood. As the availability of partial or complete connectomes expands to more systems and species4-8 it becomes critical to understand how this detailed anatomical information can inform our understanding of large-scale circuit function.9,10 Here, we use data from the Drosophila connectome4 in conjunction with whole-brain in vivo imaging11 to relate structural and functional connectivity in the central brain. We find a strong relationship between resting-state functional correlations and direct region-to-region structural connectivity. We find that the relationship between structure and function varies across the brain, with some regions displaying a tight correspondence between structural and functional connectivity whereas others, including the mushroom body, are more strongly dependent on indirect connections. Throughout this work, we observe features of structural and functional networks in Drosophila that are strikingly similar to those seen in mammalian cortex, including in the human brain. Given the vast anatomical and functional differences between Drosophila and mammalian nervous systems, these observations suggest general principles that govern brain structure, function, and the relationship between the two.