Abnormal connectivity patterns have frequently been reported as involved in pathological mental states. However, most studies focus on "static," stationary patterns of connectivity, which may miss crucial biological information. Recent methodological advances have allowed the investigation of dynamic functional connectivity patterns that describe non-stationary properties of brain networks. Here, we introduce a novel graphical measure of dynamic connectivity, called time-varying eigenvector centrality (tv-EVC). In a sample 655 children and adolescents (7-15 years old) from the Brazilian "High Risk Cohort Study for Psychiatric Disorders" who were imaged using resting-state fMRI, we used this measure to investigate age effects in the temporal in control and default-mode networks (CN/DMN). Using support vector regression, we propose a network maturation index based on the temporal stability of tv-EVC. Moreover, we investigated whether the network maturation is associated with the overall presence of behavioral and emotional problems with the Child Behavior Checklist. As hypothesized, we found that the tv-EVC at each node of CN/DMN become more stable with increasing age (P < 0.001 for all nodes). In addition, the maturity index for this particular network is indeed associated with general psychopathology in children assessed by the total score of Child Behavior Checklist (P = 0.027). Moreover, immaturity of the network was mainly correlated with externalizing behavior dimensions. Taken together, these results suggest that changes in functional network dynamics during neurodevelopment may provide unique insights regarding pathophysiology. Hum Brain Mapp, 2015. © 2015 Wiley Periodicals, Inc.