It is known that features of stimuli in the environment affect the strength of functional connectivity in the human brain. However, investigations to date have not converged in determining whether these also impact functional networks' global features, such as modularity strength, number of modules, partition structure, or degree distributions. We hypothesized that one environmental attribute that may strongly impact global features is the temporal regularity of the environment, as prior work indicates that differences in regularity impact regions involved in sensory, attentional and memory processes. We examined this with an fMRI study, in which participants passively listened to tonal series that had identical physical features and differed only in their regularity, as defined by the strength of transition structure between tones. We found that series-regularity induced systematic changes to global features of functional networks, including modularity strength, number of modules, partition structure, and degree distributions. In tandem, we used a novel node-level analysis to determine the extent to which brain regions maintained their within-module connectivity across experimental conditions. This analysis showed that primary sensory regions and those associated with default-mode processes are most likely to maintain their within-module connectivity across conditions, whereas prefrontal regions are least likely to do so. Our work documents a significant capacity for global-level brain network reorganization as a function of context. These findings suggest that modularity and other core, global features, while likely constrained by white-matter structural brain connections, are not completely determined by them.