Insomnia affects a vast population of the world and can have a wide range of causes. Existing treatments for insomnia have been linked with many side effects like headaches, dizziness, etc. As such, there is a clear need for improved insomnia treatment. Brain modelling has helped with assessing the effects of brain pathology on brain network dynamics and with supporting clinical decisions in the treatment of Alzheimer's disease, epilepsy, etc. However, such models have not been developed for insomnia. Therefore, this project attempts to understand the characteristics of the brain of individuals experiencing insomnia using continuous long-duration EEG data. Brain networks are derived based on functional connectivity and spatial distance between EEG channels. The power spectral density of the channels is then computed for the major brain wave frequency bands. A graph convolutional neural network (GCNN) model is then trained to capture the functional characteristics associated with insomnia and configured for the classification task to judge performance. Results indicated a 50-second non-overlapping sliding window was the most suitable choice for EEG segmentation. This approach achieved a classification accuracy of 70% at window level and 68% at subject level. Additionally, the omission of EEG channels C4-P4, F4-C4 and C4-A1 caused higher degradation in model performance than the removal of other channels. These channel electrodes are positioned near brain regions known to exhibit atypical levels of functional connectivity in individuals with insomnia, which can explain such results.