Eulerian cycle spectrum as molecular descriptor : a structured redundancy analysis on the TDC ADMET benchmark

Molecular property prediction for ADMET (absorption, distribution, metabolism, ex-cretion, toxicity) relies on molecular descriptors whose information content varies with the property of interest. We introduce the Eulerian cycle spectrum (ECS), a family of topological graph features derived from the Laplacian and signless Laplacian spectra of molecular graphs, and evaluate its predictive value on the Therapeutics Data Commons ADMET benchmark (22 standardised datasets, 80,455 molecules). Using LightGBM with the o cial TDC scaffold split and ve-seed protocol, we test ten feature con gurations including three ablation groups (cycle enumeration, graph fragility, and spectral analysis) against Morgan fingerprint and RDKit2D baselines. ECS combined with Morgan ngerprints improves prediction on 10 of 22 tasks, with notable gains on aqueous solubility (MAE 0.958 vs 1.210, ∆+0.252) and Caco-2 permeability (MAE 0.345 vs 0.514, ∆+0.169), but is largely redundant with RDKit2D descriptors (8/22 improved, mean ∆ = −0.003). Ablation analysis reveals that no single feature group dominates; the full ECS set outperforms each subgroup in isolation. Two novel interpretable descriptors emerge: N6/m (benzene cycle density, top-5 feature on 8/22 datasets) and ρ(L,Q) (rank correlation between Laplacian and signless Laplacian node criticality, top-20 on 6/22 datasets including #1 on volume of distribution). These ndings characterise ECS as complementary to local fingerprints and redundant with global 2D descriptors, with targeted value for solubility, permeability, and pharmacokinetic property prediction.