The use of transformation techniques (such as a wavelet transform, Fourier transform, or hybrid transform) to detect epileptic seizures by means of EEG signals is not adequate because these signals have a nonstationary and nonlinear nature. This paper reports on the design of a novel technique based, instead, on the domain of graphs. The dimensionality of each single EEG channel is reduced using a segmentation technique, and each EEG channel is then mapped onto an undirected weighted graph. A set of structural and topological graph characteristics is extracted and investigated, and several machine learning techniques are utilized to categorize the graph’s attributes. The results demonstrate that the use of graphs improves the quality of epileptic seizure detection. The proposed method can identify EEG abnormities that are difficult to detect accurately using other transformation techniques, especially when dealing with EEG big data.