Analyzing the graph based on EEG signals is always a promising and under-study for researchers and clinicians to gain the invaluable insights into the structure, dynamics, behavior and functional connectivity patterns of the brain under epilepsy conditions. The graphical features help to identify the intricate relationships or dependencies that exist among different nodes of an EEG signals-based graph, which are not apparent from traditional EEG analysis techniques that are based on individual data points. This research aims to introduce a novel feature named Normalized Weighted Forgotten Topological Index (NWFT-index) for Weighted EEG Graph (WEG) and to explore its classification performance with five different classifiers (Decision Tree, Random Forest, Gradient Boosting, SVM and k-NN. The proposed framework is investigated on Bonn university EEG epileptic data sets, the newly developed feature NWFT-index was able to capture the complex relationship between the nodes of WEG and enhance the classification performance for different test cases of Bonn EEG data sets. The framework has produced the higher classification performance results in terms of accuracy, precision, recall and F1-score metrics. In future, we will explore how NWFT-index contributing to EEG data of other neurological conditions such as Autism etc. This research explored that higher NWFT-index signifies epileptic condition (relevant to hyperconnectivity).