Vagus Nerve Stimulation (VNS) is treatment of refractory epilepsy; however, its physiological mechanism has not been fully understood. The effectiveness of VNS for each patient cannot be predicted preoperatively. Thus, the mechanism of VNS needs to be investigated in order to avoid ineffective operations. Because an epileptic seizure is caused by the spread of excessive discharge from neurons in the cerebrum, analyzing effects of VNS on electroencephalogram (EEG) would be useful for VNS mechanism investigation. In the present work, the EEG data of epileptic patients with VNS were analyzed by using Granger Causality (GC) and the graph theory. Since GC is an index which expresses the intensity of a causal relation between two time series, it may illustrate information interactions between EEG channels. In addition, a directed graph constructed from those GC values would express neural connection. The analysis was carried out with the EEG data of two patients with frontal lobe epilepsy receiving the VNS therapy. The result supported the existing hypothesis indicating the bilateral asymmetry of the VNS effect on the brain, and furthermore, it suggested that VNS would increase neural connection between the frontal lobe and other brain regions, and that should control epileptic seizures by keeping patients awake.