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Whole-brain network analysis is commonly used to investigate the topology of the brain in a variety of neuroimaging modalities. This approach is notable for its applicability to a large number of domains, such as understanding how brain network organization relates to cognition and behavior, examining disrupted brain network organization in disease, and assessing developmental trajectories across the lifespan. A benefit to this approach is the ability to summarize overall brain network organization with a single number (e.g., global efficiency). However, important local differences in network structure might exist without any corresponding observable differences in overall topology, making a whole-brain analysis strategy unlikely to detect relevant local findings. Here, we propose the network-based statistic (NBS) jackknife as a means of combining the utility of global network analysis strategies with the ability to detect relevant local differences in network structure. We describe the NBS jackknife framework, and demonstrate two specific testing scenarios in a series of examples. Finally, we provide an empirical example comparing global efficiency between children with ADHD and typically developing (TD) children. We demonstrate using functional connectivity data that there are no group differences in whole-brain global efficiency. Using the NBS jackknife, however, we identify group differences in global efficiency specific to subcortical subnetworks. The NBS jackknife framework has been implemented in a public, open source R package, netjack, available at https://cran.r-project.org/package=netjack.