Learning the Graphical Nature of Symmetries
Finite groups are rigid algebraic objects, whose Cayley graphs expose a rich network geometry through which group-theoretic structure can be measured, compared, and learned. In this paper, a dataset of $131{,}406$ Cayley graphs is constructed, covering all groups of order at most $767$ except order $512$, recording exact algebraic labels for group properties together with a broad collection of graph, cycle, distance, and spectral statistics. This census aims to provide novel benchmarks for studying how finite-group properties are reflected in Cayley graph observables. It also yields new enumerative contributions: alongside recovering known OEIS sequences for standard group classes, new se...
| Authors | Rashid Barket, Enrico Grimaldi, Yacoub Hendi et al. |
|---|---|
| Primary category | stat.ML |
| Published | 13 July 2026 |
| Last updated at source | 13 July 2026 |
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