Scalable Hierarchical Graph Generation via Soft Community Structure

Graph Neural Networks (GNNs) are powerful models for handling attributed graphs in tasks such as classification, link prediction, and community detection, as they enable the aggregation of information from both structural and semantic sources. However, progress in community detection is hindered by the lack of high-quality datasets, since ground-truth community labels are often unavailable and most algorithms proposed in recent literature rely on the same benchmark datasets for model training and evaluation. To address this issue, attributed random graph generators are commonly employed to create synthetic graphs for assessing the strengths and limitations of GNN-based models. Nevertheless, most existing generators rely heavily on power-law degree distributions, despite recent evidence indicating that scale-free networks are rare, particularly in social network contexts. Moreover, state-of-the-art attributed graph generators provide limited flexibility, as they do not allow users to construct communities with varying densities, degree distributions, and sub-community structures. To overcome these limitations, we introduce the Synthetic Community-Aware Attributed Graph Generator (SynCo), a graph generation algorithm that allows users to control the node degree distribution and sub-community structure. We evaluate SynCo across three different tasks: graph mimicking, hyperparameter evaluation, and node clustering tuning. The results show that our model outperforms state-of-the-art approaches in synthetic graph generation and data augmentation, while preserving the original distributions of duplicated and augmented datasets, as confirmed by statistical tests well know in literature. We also demonstrate the ability of SynCo to generate nodes in large scale, up to 2.1 million nodes.

Graphs provide a natural representation of many complex systems, ranging from social platforms to ecosystems. However, the development of graph-based machine learning methods is often constrained by the limited availability of large and diverse graph datasets. In this paper, we introduce $\texttt{DCBA}$, a model-based approach to graph data augmentation that infers the configuration of a synthetic graph generator from an observed network. We instantiate the proposed framework using the $\texttt{ABCD}$ generator, which produces scale-free networks with community structure. Our model learns a joint representation of graphs and generator parametrisations using a multi-positive contrastive objective with soft negative weighting. The learned representation enables the prediction of an $\texttt{ABCD}$ configuration whose stochastic realisations preserve the macrostructural properties encoded by the generator. Experiments show that $\texttt{DCBA}$ recovers generator parameters more accurately and robustly than an algorithmic inverse-modelling baseline. Its downstream utility is further demonstrated in community detection, where inferred configurations used to fine-tune $\texttt{PRoCD}$ improve AMI on average by $161\%$ on synthetic and $273\%$ on real-world networks.

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.