Advances in network science and computer engineering have enabled brain connectivity analysis using clinical big data such as brain magnetic resonance imaging (MRI), electroencephalography (EEG), or magnetoencephalography (MEG). Resting-state functional connectivity analysis aims to reveal the characteristics of functional brain network in various diseases and normal brain maturation using resting-state EEG. Simplified sequence of resting-state functional connectivity analysis methods will be reviewed in this article. The outcomes from EEG resting-state connectivity analysis are comprised of connectivity itself of the specific condition and the network topology measure which describe the characteristics of specific connectivity. An increasing number of studies report the differences in the functional connection itself, global network measures including segregation (connectedness), integration (efficiency), and importance of specific nodes (centrality or node degree). Several issues that are relevant in the resting-state connectivity analysis are obtaining good quality EEG for analysis, consideration of particular features of EEG signal, understanding different types of association measures, and statistics for comparison of connectivities. Well-designed and carefully analyzed EEG resting-state connectivity analysis can provide useful information for patient care in pediatric neurology.