Extremely Fast and Compact Binary Graph Representations via Randomized Operator Sketching

Graph neural networks typically rely on dense, floating-point node representations, which can impose substantial memory and computational costs. Binary graph hashing offers an alternative by encoding node information as compact bit strings. However, existing approaches either sacrifice global topological information for computational efficiency or incur substantial generation costs. We introduce an ultra-fast, entirely algebraic hashing method that constructs binary node representations directly from graph structure, without requiring node features or gradient-based training. Our method approximates a high-order structural transition matrix using randomized column sampling inspired by the Nystr"om method and combines it with an efficient label-safe semantic propagation mechanism. The resulting continuous representations are discretized through column-wise thresholding to obtain compact binary codes. Experiments on ten node classification datasets show that the proposed method consistently improves classification accuracy over existing feature-free binary baselines while requiring sub-second code generation on many datasets. The resulting binary representations are also naturally suited to event-driven computation, making them compatible with neuromorphic spiking neural networks and gradient-free learning rules. These results demonstrate that simple algebraic approximations can provide an efficient alternative to learned pipelines for discrete graph representation learning.