The human brain is one of the most complex biological systems. Neuro scientists seek to understand the brain function through detailed analysis of neuronal excitability and synaptic transmission. In this study, we propose a network analysis framework to study the evolution of epileptic seizures. We apply a signal processing approach, derived from information theory, to investigate the synchronization of neuronal activities, which can be captured by electroencephalogram (EEG) recordings. Two network-theoretic approaches are proposed to globally model the synchronization of the brain network. We observe some unique patterns related to the development of epileptic seizures, which can be used to illuminate the brain function governed by the epileptogenic process during the period before a seizure. The proposed framework can provide a global structural patterns in the brain network and may be used in the simulation study of dynamical systems (e.g. the brain) to predict oncoming events (e.g. seizures). To analyze long-term EEG recordings in the future, we discuss how the Markov-Chain Monte Carlo (MCMC) methodology can be applied to estimate the clique parameters. This MCMC framework fits very well with this work as the epileptic evolution can be considered to be a system with unobservable state variables and nonlinearities.