To study the differences in functional brain networks between eyes-closed (EC) and eyes-open (EO) at resting state, electroencephalographic (EEG) activity was recorded in 21 normal adults during EC and EO states. The synchronization likelihood (SL) was applied to measure correlations between all pairwise EEG channels, and then the SL matrices were converted to graphs by thresholding. Graphs were measured by topological parameters in theta (4-7 Hz), alpha (8-13 Hz), and beta (14-30 Hz) bands. By changing from EC to EO states, mean cluster coefficients decreased in both theta and alpha bands, but mean shortest path lengths became shorter only in the alpha band. In addition, local efficiencies decreased in both theta and alpha bands, while global efficiencies in the alpha band increased inversely. Opening the eyes decreased both nodes and connections in frontal area in the theta band, and also decreased those in bilateral posterior areas in the alpha band. These results suggested that a combination of the SL and graph theory methods may be a useful tool for distinguishing states of EC and EO. The differences in functional connectivity between EC and EO states may reflect the difference of information communication in human brain.