Denoising diffusion generative models are state-of-the-art methods for generating synthetic images that have also proved successful in tabular and graph synthetic data generation. However, their computational complexity has limited the application of these techniques to graph data, focusing usually on smaller graphs, such as those used in molecular modeling. In this paper, we propose SaGess, a discrete denoising diffusion approach, which is able to generate large real-world networks. Through a generalized divide-and-conquer framework, SaGess overcomes the scaling limitations of the diffusion model DiGress, by sampling a covering of subgraphs of the initial graph, training a DiGress module, and finally reconstructing a synthetic graph using the subgraphs that have been generated using the DiGress module. We evaluate the quality of the synthetic data sets against several competitor methods by comparing graph statistics between the original and synthetic samples, as well as evaluating the utility of the synthetic data set produced by using it to train a task-driven model, namely link prediction. In our experiments, SaGess  outperforms most of the one-shot state-of-the-art graph generating methods by a significant factor, both on the graph metrics and on the link prediction task.