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Nonrapid eye movement (NREM) sleep is associated with fading consciousness in humans. Recent neuroimaging studies have demonstrated the spatiotemporal alterations of the brain functional connectivity (FC) in NREM sleep, suggesting the changes of information integration in the sleeping brain. However, the common stationarity assumption in FC does not satisfactorily explain the dynamic process of information integration during sleep. The dynamic FC (dFC) across brain networks is speculated to better reflect the time‐varying information propagation during sleep. Accordingly, we conducted simultaneous EEG‐fMRI recordings involving 12 healthy men during sleep and observed dFC across sleep stages using the sliding‐window approach. We divided dFC into two aspects: mean dFC (dFCmean) and variance dFC (dFCvar). A high dFCmean indicates stable brain network integrity, whereas a high dFCvar indicates instability of information transfer within and between functional networks. For the network‐based dFC, the dFCvar were negatively correlated with the dFCmean across the waking and three NREM sleep stages. As sleep deepened, the dFCmean decreased (N0~N1 > N2 > N3), whereas the dFCvar peaked during the N2 stage (N0~N1 < N3 < N2). The highest dFCvar during the N2 stage indicated the unstable synchronizations across the entire brain. In the N3 stage, the overall disrupted network integration was observed through the lowest dFCmean and elevated dFCvar, compared with N0 and N1. Conclusively, when the network specificity (dFCmean) breaks down, the consciousness dissipates with increasing variability of information exchange (dFCvar). [ABSTRACT FROM AUTHOR]