Lesion and functional neuroimaging evidence suggest that local network deficits can be compensated by global network over-recruitment during a cognitive task. However, the neural mechanisms linking local and global network changes remain uncertain. To investigate this issue, we manipulated local function using repetitive transcranial magnetic stimulation (rTMS) and measured structural and task-based functional network organization during memory encoding. The study yielded two main findings. First, consistent with the compensation hypothesis, 1-Hz rTMS attenuated local activity in the stimulated left prefrontal cortex (PFC) but increased the connectivity of this region with other brain areas, including contralateral PFC. Second, this 1-Hz-related increase in global connectivity effects was associated with the volume of more global connections, suggesting white-matter constraints adaptive changes in functional connectivity. Taken together, these results clarify the neural mechanisms linking local and global network changes and the role of structural connectivity.