Healthy brain function is marked by neuronal network dynamics at or near the critical phase, which separates regimes of instability and stasis. A failure to remain at this critical point can lead to neurological disorders such as epilepsy, which is associated with pathological synchronization of neuronal oscillations. Using full Hodgkin-Huxley (HH) simulations on a Small-World Network, we are able to generate synthetic electroencephalogram (EEG) signals with intervals corresponding to seizure (ictal) or non-seizure (interictal) states that can occur based on the hyperexcitability of the artificial neurons and the strength and topology of the synaptic connections between them. These interictal simulations can be further classified into scale-free critical phases and disjoint subcritical exponential phases. By changing the HH parameters, we can model seizures due to a variety of causes, including traumatic brain injury (TBI), congenital channelopathies, and idiopathic etiologies, as well as the effects of anticonvulsant drugs. The results of this work may be used to help identify parameters from actual patient EEG or electrocorticographic (ECoG) data associated with ictogenesis, as well as generating simulated data for training machine-learning seizure prediction algorithms.