Shape-Matched Evaluation of Returned SEGO Coding Trees on Molecular Scaffold Shift

Recognizing molecules with unfamiliar core frameworks is an important task for molecular property models. Hierarchical graph representations organize vertices into nested groups. Their detection performance, however, leaves open what the chosen groups reveal beyond the hierarchy's shape. We introduce a comparison that preserves group sizes and branching while randomizing vertex membership. We apply it to coding trees from a structural entropy guided graph detector and evaluate the edges retained within groups before representation learning. On molecular scaffold splits, these summaries yield positive average ranking gains over the random reference. The evidence depends on the detector and on how the reference is estimated: repeated evaluations retain positive means at the original randomization budget, while larger ensembles leave the gain uncertain. This comparison helps distinguish information in the chosen groups from that captured by a hierarchy of the same shape. The core code is provided in the supplementary material.