Electroencephalography (EEG) is a technology for measuring brain neuronal activity and is used to investigate various pathological conditions of the brain. A brain can be viewed as a complex network of neurons. A brain functional network represents quantitative interactions among EEG channels and can be expressed as a graph. Graph theoretical analysis, therefore, can be applied to offer a broader scope to inspect the global functional network characteristics of epileptic brains and can reveal the existence of small-world network structure. In this study, we inspected the interhemispheric power asymmetry (IHPA) of interictal scalp EEG signals recorded from patients with epilepsy and psychogenic nonepileptic events and found significant differences between the two patient groups. Specifically, the degrees of IHPA in the two patient groups differed in signals from the frontal lobe regions in the delta, theta, alpha, and gamma frequency bands.