Feature-Aware (Hyper)graph Generation via Next-Scale Prediction

Graph generative models perform well on small structured data but struggle to scale to large, complex structures. Hierarchical approaches improve scalability but often ignore node and edge features, which are critical in real-world applications, particularly for hypergraphs that model higher-order relationships. In this paper, we propose FAHNES (feature-aware (hyper)graph generation via next-scale prediction), a hierarchical framework that jointly generates topology and features for graphs and hypergraphs. FAHNES builds multi-scale representations through node coarsening and localized expansion, guided by a novel hierarchical scale encoding that controls granularity and ensures cross-scale consistency. Experiments on synthetic, 3D mesh, and graph point cloud datasets demonstrate competitive or state-of-the-art performance while uniquely scaling to featured large-scale graphs and hypergraphs. Our code is open source.

Traditional methods for generating graphs and hypergraphs become computationally expensive as graph size grows, making it difficult to model the large-scale structures that matter most in real-world applications. Recent hierarchical approaches improved scalability by generating graph topology efficiently, but they focused only on connectivity patterns and could not generate node features such as 3D coordinates or semantic types. In this work, we take a first step toward addressing this limitation by extending hierarchical graph generation to include node features. This enables preliminary results on 3D mesh and point cloud generation using a single unified graph-based framework, rather than relying on task-specific architectures.