['To analyze the functional connectivity patterns of the different EEG bands during wakefulness and sleep (different sleep stages and cyclic alternating pattern (CAP) conditions), using concepts derived from Graph Theory.', 'We evaluated spatial patterns of EEG band synchronization between all possible pairs of electrodes (19) placed over the scalp of 10 sleeping healthy young normal subjects using two graph theoretical measures: the clustering coefficient (Cp) and the characteristic path length (Lp). The measures were obtained during wakefulness and the different sleep stages/CAP conditions from the real EEG connectivity networks and randomized control (surrogate) networks (Cp-s and Lp-s).', 'We found values of Cp and Lp compatible with a small-world network organization in all sleep stages and for all EEG bands. All bands below 15Hz showed an increase of these features during sleep (and during CAP-A phases in particular), compared to wakefulness.'] Does the functional connectivity of different EEG bands move towards small-world network organization during sleep?