xVGAE: A Hierarchical Variational Graph Autoencoder for Exchangeable Graphs

Graph foundation models need a discrete token representation, but casting a graph as a generatable token sequence faces a structural obstacle: edges spanning beyond the serialization window cannot be emitted in one pass--so one-pass autoregressive generators systematically under-produce cycles--and a single global condition cannot tell candidate edges apart. GraphVQ removes both obstacles: node contexts--features plus a local edge mask under multi-order breadth-first serialization--are quantized into a shared codebook by a VQ-VAE with BCE-calibrated Bernoulli edge decoding, and a second-stage structure-aware decoder emits the global adjacency conditioned on token-derived pair features, whose necessity over any global-summary condition is formalized in a scoped impossibility result. The tokenizer reconstructs node features at 0.86--0.99 accuracy and decodes local edges at AUROC >= 0.89 (ECE <= 0.007). Under one same-split protocol on four datasets, pair conditioning improves orbit MMD 0.248 -> 0.174 on PROTEINS and 3.4x on a ring stress test, and vanishes on a random-label control--the signature of attribute--topology coupling--so the gain is claimed exactly where attributes carry edge-relevant signal. GraphVQ ranks first among learned generators on PROTEINS, ties for first on SYN-COMM, and improves orbit MMD 2.7--17x over one-stage generation on three datasets, with seed-level bootstrap intervals confirming the rankings are not seed noise; on MUTAG the unweighted edge target under-generates and is reported as such. These results locate the structural control of autoregressive graph generation in the granularity of the condition: pair-level token context turns a quantized vocabulary into a usable capacity axis for distribution-faithful graph generation and future token-level pretraining.

Generating realistic and diverse graphs is a key problem in machine learning, with applications in molecular discovery, circuit design, cybersecurity, and beyond. However, current graph generative models remain limited by scalability and novelty. Diffusion-based methods often require costly full-adjacency operations and long denoising chains, while many autoregressive and hybrid models have at least quadratic complexity. In addition, these models often imitate training graphs rather than generalize beyond them. We propose a lightweight autoregressive framework to address these issues. It uses a structure-guided topological ordering to serialize graphs into regular edge sequences, enabling near log-linear generation, and a two-phase training strategy that combines exploration-oriented augmentation with iterative refinement to reduce overfitting and promote controlled novelty. Experiments on molecular and non-molecular benchmarks show that our approach improves novelty while preserving high validity and uniqueness. The framework also supports both LSTM and Mamba-style causal sequence backbones, with large-memory accelerators enabling longer graph-sequence experiments beyond typical GPU limits.

Graph generation models have advanced significantly with deep learning, yet they remain limited in scalability, flexibility, and ability to model underlying structures. We present GraphK, a novel encoder-sampler-decoder framework for graph generation that overcomes these challenges through structural flexibility and computational efficiency. Unlike autoregressive approaches constrained by vocabulary size (i.e. number of nodes in graph generation), GraphK allows for both upscaling (generating graphs with more nodes than the input) and downscaling, providing a flexible control over output graph size. By learning permutation-invariant latent representations and sampling new node embeddings via maximum likelihood estimation, GraphK generalizes across graph sizes and structures. For edge generation, we employ edge prediction with a KDTree-based top-k neighbor search in the latent space, reducing computational cost. Based on the manifold smoothness assumption, our method effectively captures graph properties. Experiments on synthetic and real-world datasets show that GraphK outperforms existing methods, accurately learns graph structures, and generates synthetic graphs without explicit definitions.