This study aimed to investigate differences in brain networks between healthy children and children with attention deficit hyperactivity disorder (ADHD) during an attention test. To fulfill this, we constructed weighted directed graphs based on Electroencephalography (EEG) signals of 61 children with ADHD and 60 healthy children with the same age. Nodes of graphs were 19 EEG electrodes, and the edges were phase transfer entropy (PTE) between each pair of electrodes. PTE is a measure for directed connectivity that determines the effective relationship between signals in linear and nonlinear coupling. Connectivity graphs of each sample were constructed using PTE in the five frequency bands as follows: delta, theta, alpha, beta, and gamma. To investigate the differences in connectivity strength of each node after the sparsification process with two values (0.5 and 0.25), the permutation statistical test was used with the statistical significance level of p<0.01. The results indicate stronger inter-regional connectivity in the prefrontal brain regions of the control group compared to the ADHD group. However, the strength of inter-regional connectivity in the central regions of the ADHD group was higher. A comparison of the prefrontal regions between the two groups revealed that the areas of the Fp1 electrode (left prefrontal) in healthy individuals play stronger transmission roles. Our research can provide new insights into the strength and direction of connectivity in ADHD and healthy individuals during an attention task.