Graph theoretical analysis has recently been used to study brain function. This study aims to compare the functional brain networks derived from electroencephalography (EEG) of 10 patients suffering from epilepsy with 10 healthy subjects based on graph theory. Five epochs per healthy subject, and ten epochs (during epileptiform discharge and non-discharge) per patient were selected and analyzed using wavelet-crosscorrelation analysis. The clustering coefficient, characteristic path length, small-worldness, and nodal betweenness centrality were calculated using graph analysis. The results showed that in the patients, Wavelet-crosscorrelation Coefficients (WCC) were significantly higher, and clustering and path length were significantly lower during discharge compared with the healthy subjects, along with alterations in the hub regions. These results suggest a loss of small-world topology in the functional brain network of epilepsy patients. A loss of small-world topology was found even during non-discharge, therefore network indices might aid to distinguish epilepsy patients from healthy individuals.