The brain connectivity is known to have substantial influences over the brain function and its underlying information processes. In this chapter, a novel graphtheoretic approach is introduced to investigate the connectivity among brain regions through electroencephalogram (EEG) recordings acquired from a patient with mesial temporal lobe epilepsy (MTLE). The first step of the proposed approach is to transform the brain connectivity behavior into a complete graph. The connectivity for each pair of the brain regions is first quantified by the cross mutual information (CMI) measure, and then the maximum clique algorithm is subsequently applied to find the clique that contained a group of highly connected brain regions that is represented by a clique with maximum size. The CMI is known to have the ability to capture the connectivity between EEG signals. The adopted maximum clique algorithm can reduce the complexity of the clustering procedure for finding the maximum connected brain regions. The proposed graph-theoretic approach offers better assessments to visualize the structure of the brain connectivity over time. The results indicate that the maximum connected brain regions prior to seizure onsets were where the impending seizure was initiated. Furthermore, the proposed approach may be used to improve the outcome of the epilepsy surgery by identifying the seizure onset region(s) correctly.