Epilepsy is a neurological disorder identified by sudden and recurrent seizures, which are believed to be accompanied by distinct changes in brain dynamics. Exploring the dynamic changes of brain network states during seizures can pave the way for improving the diagnosis and treatment of patients with epilepsy. In this paper, the connectivity brain network is constructed using the phase lag index (PLI) measurement within five frequency bands, and graph-theoretic techniques are employed to extract topological features from the brain network. Subsequently, an unsupervised clustering approach is used to examine the state transitions of the brain network during seizures. Our findings demonstrate that the level of brain synchrony during the seizure period is higher than the pre-seizure and post-seizure periods in the theta, alpha, and beta bands, while it decreases in the gamma bands. These changes in synchronization also lead to alterations in the topological features of functional brain networks during seizures. Additionally, our results suggest that the dynamics of the brain during seizures are more complex than the traditional three-state model (pre-seizure, seizure, and post-seizure) and the brain network state exhibits a slower rate of change during the seizure period compared to the pre-seizure and post-seizure periods.