Electroencephalogram (EEG) signal analysis plays a significant role in recognizing brain function and supporting the diagnosis of Epilepsy. Existing graph approaches are binary or use endpoint-only (slope/correlation) weights that do not capture the interior fluctuations and trend departures, which limit robustness for epilepsy detection. Many rely heavily on preprocessing and lack shift/scale robustness, which compromises generalization and reliability across subjects and recording conditions. The research aims to propose a novel SXTD-Weighted Visibility Graph framework with an information-rich edge weighting scheme to enhance interpretability and diagnostic accuracy in epilepsy EEG analysis. In addition, new EEG graph features such as Transitive Amplification Index (TAI), MedianWeightEps are developed that capturing the interior fluctuations and trend deviations, remaining shift-invariant and scale-equivariant, providing tunable noise–structure control, and requiring no additional assumptions. The proposed framework achieved 100% accuracy, precision, recall, and specificity across all binary test cases (A–E vs. E) when investigated using multiple classifiers on the Bonn University epileptic EEG dataset. Short, quick EEG changes (spikes, sharp waves) are regularly amplified by the framework, providing a clear difference between ictal and non-ictal segments.