Epilepsy is one of the most chronic brain disorder recorded from since 2000 BC. Almost one-third of epileptic patients experience seizures attack even with medicated treatment. The menace of SUDEP (Sudden unexpected death in epilepsy) in an adult epileptic patient is approximately 8-17% more and 34% in a children epileptic patient. The expert neurologist manually analyses the Electroencephalogram (EEG) signals for epilepsy diagnosis. The non-stationary and complex nature of EEG signals this task more error-prone, time-consuming and even expensive. Hence, it is essential to develop automatic epilepsy detection techniques to ensure an appropriate identification and treatment of this disease. Nowadays, graph-theory has been considered as a prominent approach in the neuroscience field. The network-based approach characterizes a hidden sight of brain activity and brain-behavior mapping. The graph-theory not even helps to understand the underlying dynamics of EEG signals at microscopic, mesoscopic, and macroscopic level but also provide the correlation among them. This paper provides a review report about graph-theory based automated epilepsy detection methods. Furthermore, it will assist the expert's neurologist and researchers with the information of complex network-based epilepsy detection and aid the technician for developing an intelligent system that improving the diagnosis of epilepsy disorder.