The longstanding dichotomy between the concepts of “focal” and “primary generalized” epilepsy has become increasingly blurred, raising fundamental questions about the nature of ictal onset in localized brain regions versus large-scale brain networks. We hypothesize that whether an EEG discharge appears focal or generalized is driven by the pattern of connections in brain networks, irrespective of the presence of focal brain abnormality. Using a computational model of a simple “brain” consisting of four regions and the connections between them, we explored the effects of altering connectivity structure versus the effects of introducing an “abnormal” brain region, and the interactions between these factors. Computer simulations demonstrated that electroencephalography (EEG) discharges representing either generalized or focal seizures arose purely as a consequence of subtle changes in network structure, without the requirement for any localized pathologic brain region. Furthermore we found that introducing a pathologic region gave rise to focal, secondary generalized, or primary generalized seizures depending on the network structure. Counterintuitively, we found that decreasing connectivity between regions of the brain increased the frequency of seizure-like activity. Our findings may enlighten current controversies surrounding the concepts of focal and generalized epilepsy, and help to explain recent observations in genetic animal models and human epilepsies, where loss of white matter pathways was associated with the occurrence of seizures.