This study presents a methodology developed for estimating effective connectivity in brain networks (BNs) using multichannel scalp EEG recordings. The methodology uses transfer entropy as an information transfer measure to detect pair-wise directed information transfer between EEG signals within 6, 0, alpha, /3 and gamma-bands. The developed methodology is then used to study the properties of directed BNs in children with attention-deficit hyperactivity disorder (ADHD) and compare them with that of the healthy controls using both statistical and receiver operating characteristic (ROC) analyses. The results indicate that directed information transfer between scalp EEG electrodes in the ADHD subjects differs significantly compared to the healthy ones. The results of the statistical and ROC analyses of frequency-specific graph measures demonstrate their highly discriminative ability between the two groups. Specifically, the graph measures extracted from the estimated directed BNs in the beta-band show the highest discrimination between the ADHD and control groups. These findings are in line with the fact that /3-band reflects active concentration, motor activity, and anxious mental states. The reported results show that the developed methodology has the capacity to be used for investigating patterns of directed BNs in neuropsychiatric disorders.