A new nonlinear approach is presented for high-frequency electrocorticography (ECoG)-based diagnosis of epilepsy. The ECoG data from 3 patients with epilepsy are analyzed in this study. A recently developed algorithm in graph theory, visibility graph (VG), is applied in this research. The approach is based on the key discovery that high-frequency oscillation takes place during epileptic seizure, making it a marker of epilepsy. Therefore, the nonlinear property of the high-frequency signal may be more noticeable. Hence, a complexity measure, called graph index complexity (GIC), is computed using the VG of the patients' high-frequency ECoG subband. After comparison and statistical analysis, the nonlinear feature is proved to be effective in detection and location of the epilepsy. Two different traditional complexities, sample entropy and Lempel-Ziv, were also calculated to make a comparison and prove that GIC provides better identification.