There is extensive evidence that functional organization of the human brain varies dynamically as the brain switches between task demands, or cognitive states. This functional organization also varies across subjects, even when engaged in similar tasks. To date, the functional network organization of the brain has been considered static. In this work, we use fMRI data obtained across multiple cognitive states (task-evoked and rest conditions) and across multiple subjects, to measure state- and subject-specific functional network parcellation (the assignment of nodes to networks). Our parcellation approach provides a measure of how node-to-network assignment (NNA) changes across states and across subjects. We demonstrate that the brain’s functional networks are not spatially fixed, but that many nodes change their network membership as a function of cognitive state. Such reconfigurations are highly robust and reliable to the extent that they can be used to predict cognitive state with up to 97% accuracy. Our findings suggest that if functional networks are to be defined via functional clustering of nodes, then it is essential to consider that such definitions may be fluid and cognitive-state dependent.