It has been revealed that spontaneous coherent brain activity during rest, measured by functional magnetic resonance imaging (fMRI), self-organizes a “small-world” network by which the human brain could sustain higher communication efficiency across global brain regions with lower energy consumption. However, the state-dependent dynamics of the network, especially the dependency on the conscious state, remain poorly understood. In this study, we conducted simultaneous electroencephalographic recording with resting-state fMRI to explore whether functional network organization reflects differences in the conscious state between an awake state and stage 1 sleep. We then evaluated whole-brain functional network properties with fine spatial resolution (3781 regions of interest) using graph theoretical analysis. We found that the efficiency of the functional network evaluated by path length decreased not only at the global level, but also in several specific regions depending on the conscious state. Furthermore, almost two-thirds of nodes that showed a significant decrease in nodal efficiency during stage 1 sleep were categorized as the default-mode network. These results suggest that brain functional network organizations are dynamically optimized for a higher level of information integration in the fully conscious awake state, and that the default-mode network plays a pivotal role in information integration for maintaining conscious awareness.