The organization of functional brain networks changes across human lifespan. The present study analyzed functional brain networks in healthy full-term infants (N = 139) within 1–6 days from birth by measuring neural synchrony in EEG recordings during quiet sleep. Large-scale phase synchronization was measured in six frequency bands with the Phase Lag Index. Macroscopic network organization characteristics were quantified by constructing unweighted minimum spanning tree graphs. The cortical networks in early infancy were found to be significantly more hierarchical and had a more cost-efficient organization compared with MST of random control networks, more so in the theta and alpha than in other frequency bands. Frontal and parietal sites acted as the main hubs of these networks, the topological characteristics of which were associated with gestation age (GA). This suggests that individual differences in network topology are related to cortical maturation during the prenatal period, when functional networks shift from strictly centralized toward segregated configurations. Hum Brain Mapp 38:4019–4033, 2017.