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Epilepsy has impacted more than 50 million people worldwide, and it continues to pose challenges for drug discovery. There is a dearth of reliable experimental data on antiepileptic drugs (AED) and the mechanisms of drug activity are not well understood. In the current study we develop novel mathematical tools for antiepileptic molecules as an integral part of machine learning and artificial intelligence through omega polynomials and topological indices to derive robust structure–activity relations for the correlation and prediction of anticonvulsant activities as measured by their ED 50  values. We have applied the developed mathematical and computational tools to 31 potential AEDs for the development of reliable structure–activity relations. We show using both statistical and topological tools that the developed structure–activity relations on the basis of graph theoretical tools provide a robust 3D-QSAR equation for the ED 50  prediction of AEDs with an  R  value of 0.975, and one of the key factors that determines the potency of an AED is its ability to penetrate the blood–brain–barrier (BBB).

Structure–activity relations for antiepileptic drugs through omega polynomials and topological indices