An infantile spasms syndrome is a subset of epileptic syndrome occurring in children less than two years old. Approximately two-thirds of these patients have hypsarrhythmia, whose EEG patterns display large amplitudes, multifocal sharp waves, and described as disorganization. However, there are many variations of hypsarrhythmia, and the criteria for recognizing hypsarrhythmia vary across clinicians, leading to a need for a differentiable pattern among the clinically diagnosed hypsarrhythmia patients and those without hypsarrhythmia. Patients in this study had recorded EEG of the pre- and post- treatment in both awake and sleep states. The EEG data of these patients underwent a connectivity analysis using maximum cross correlations among electrode pairs. Previous research has shown EEG connectivity leads to unique connectivity and network stability in adult patients. We incorporated these techniques to study the brain networks of children with infantile spasms. More specifically, we wanted to focus on spatial distributions of connectivity, statistical analysis on connectivity, and network stability. From our analysis, there is a statistical difference between spatial distributions of connectivity in patients of hypsarrhythmia and non-hypsarrhythmia across all states. Furthermore, there is a statistical increase in long range connections for hypsarrhythmia patients in the sleep states, both pre- and post- treatment. We are also able to note network stability with increasing temporal window size, but more stability in the pre- than post-treatment and in the sleep than awake state. This analysis is intriguing because the disorganization of hypsarrhythmia may lead to assume the networks are not stable over long periods of time.