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The current opinion in epilepsy surgery is that successful surgery is about removing pathological cortex in the anatomic sense. This contrasts with recent developments in epilepsy research, where epilepsy is seen as a network disease. Computational models offer a framework to investigate the influence of networks, as well as local tissue properties, and to explore alternative resection strategies. Here we study, using such a model, the influence of connections on seizures and how this might change our traditional views of epilepsy surgery. We use a simple network model consisting of four interconnected neuronal populations. One of these populations can be made hyperexcitable, modeling a pathological region of cortex. Using model simulations, the effect of surgery on the seizure rate is studied. We find that removal of the hyperexcitable population is, in most cases, not the best approach to reduce the seizure rate. Removal of normal populations located at a crucial spot in the network, the “driver,” is typically more effective in reducing seizure rate. This work strengthens the idea that network structure and connections may be more important than localizing the pathological node. This can explain why lesionectomy may not always be sufficient.