Objective, early, and non-invasive assessment of brain function in high-risk newborns is critical to initiate timely interventions and to minimize long-term neurodevelopmental disabilities. A prerequisite to identifying deviations from normal, however, is the availability of baseline measures of brain function derived from healthy, full-term newborns. Recent advances in functional MRI combined with graph theoretic techniques may provide important, currently unavailable, quantitative markers of normal neurodevelopment. In the current study, we describe important properties of resting state networks in 60 healthy, full-term, unsedated newborns. The neonate brain exhibited an efficient and economical small world topology: densely connected nearby regions, sparse, but well integrated, distant connections, a small world index greater than 1, and global/local efficiency greater than network cost. These networks showed a heavy-tailed degree distribution, suggesting the presence of regions that are more richly connected to others ('hubs'). These hubs, identified using degree and betweenness centrality measures, show a more mature hub organization than previously reported. Targeted attacks on hubs show that neonate networks are more resilient than simulated scale-free networks. Networks fragmented faster and global efficiency decreased faster when betweenness, as opposed to degree, hubs were attacked suggesting a more influential role of betweenness hub in the neonate network.