Numerous studies have suggested that sleep spindle waves may play a role in the hippocampal-cortical transmission of information associated with memory enhancement. In previous research, the clustering coefficient increased significantly from wakefulness to sleep, indicating that the graph theory may be able to characterize brain network activity during sleep. However, previous studies have not investigated in detail the characteristics of the brain network in individual sleep stages; the brain network activity in the EEG at each sleep stage has not yet been clarified. In this study, we compared the characteristics of the network activity in various sleep stages by determining the functional connectivity from EEG in individual stages, constructing the networks and comparing the clustering coefficients and characteristic path lengths. We found a significant decrease in the characteristic path length in LowBeta band (13–15 Hz) from Stage 1 to later stages. However, there was no significant difference in the clustering coefficient. Our results are consistent with the concept that sleep spindles are related to memory consolidation. Therefore, the results suggest that the networks generated by the brain are more efficient in middle and deep sleep.