GNN Framework Learns Algebraic Properties from Cayley Graphs

Building on previous work that used Graph Neural Networks (GNNs) to predict the solvability of finite groups, this study presents a generalized framework. The new approach allows GNNs to learn a range of algebraic properties directly from the Cayley graph representations of finite groups. This involves using a consistent GNN architecture and training methodology across different properties. The researchers tested the framework on properties like abelianity, nilpotency, and solvability, using a diverse collection of finite groups. Their results indicate that the GNN framework successfully learns and differentiates these algebraic characteristics solely from their graph-based representations. This demonstrates that Cayley graphs encode substantial algebraic information that GNNs can effectively uncover, opening new avenues for applying graph representation learning in abstract algebra.