G-NAC: Graph Neural Automata Clustering via Emergent Domain Formation

We introduce Graph Neural Automata Clustering (G-NAC), an unsupervised clustering method in which observations interact as cells on a fixed neighborhood graph. A shared recurrent graph-neural cellular rule evolves latent domain states through local interactions, which are converted into a rank-based spectral affinity for partitioning. Across 73 clustering tasks from 57 benchmark datasets, G-NAC achieved a mean adjusted Rand index (ARI) of 0.7951, comparable to Genie at 0.7941 and higher than the other evaluated baselines. Empirical training time and GPU memory scaled approximately linearly from 5,000 to 100,000 nodes. Learned transition rules also transferred from smaller source graphs to independent 100,000-node samples generated under matched conditions. These results demonstrate a recurrent graph-clustering formulation while identifying dependencies on graph quality, readout design, and source-target similarity.