A question to be addressed in the present study is how different the eyes-closed (EC) and eyes-open (EO) resting states are across frequency bands in terms of efficiency and centrality of the brain functional network. We investigated both the global and nodal efficiency and betweenness centrality in the EC and EO resting states from 39 volunteers. Mutual information was used to obtain the functional connectivity for each of the four frequency bands (theta, alpha, beta, and gamma). We showed that the cortical hubs with high betweenness centrality were maintained in the EC and EO resting states. We further showed that these hubs were associated with more than three frequency bands, suggesting that these hubs play an important role in the brain functional network at multiple temporal scales in the resting states. Enhanced global efficiency values were found in the theta and alpha bands in the EO state compared with those in the EC state. Moreover, it turned out that in the EO state the functional network was reorganized to enhance nodal efficiency at the nodes related to both the default mode and the dorsal attention networks and sensory-related resting-state networks. This result suggests that in the EO state the brain functional network was efficiently reorganized, facilitating the adaptation of the brain network to the change in state, which could help in understanding brain disorders that have a disturbance in communication with external environments by using the adaptation ability of brain functional networks.