Automatic diagnosis of epilepsy using electroencephalogram (EEG) signals is a hot topic in medical community as traditional diagnosis relies on tedious visual screening by highly trained clinicians from lengthy EEG recording. Hence, a new methodology to automatically detect epilepsy from EEG signals considering complex network as the principal dynamics of the epileptic EEG signals can be perfectly described by complex network is introduced. A novel edge weight method for visibility graph in the complex network for detection of epilepsy syndrome is presented. The effect of new edge weights for one key characteristic (such as, average weighted degree) of complex network is investigated. Finally, the extracted feature set is evaluated by two popular machine learning classifiers: support vector machine (SVM) with several kernel functions and linear discriminant analysis. The experimental results on Bonn University datasets show that the proposed approach is able to characterise the epilepsy from EEG signals generating up to 100% classification performance by SVM with polynomial kernel.