Generative models for graph data are an important research topic in machine learning.

We describe a new setting for learning a deep graph generative model (GGM) from aggregate graph statistics, rather than from the graph adjacency matrix. Matching the statistics of observed training graphs is the main approach for learning traditional GGMs (e.g, BTER, Chung-Lu, and Erdos-Renyi models). Privacy researchers have proposed learning from graph statistics as a way to protect privacy. We develop an architecture for training a deep GGM to match statistics while preserving local differential privacy guarantees. Empirical evaluation on 8 datasets indicates that our deep GGM model generates more realistic graphs than the traditional GGMs when both are learned from graph statistics only. We also benchmark our deep GGM trained on statistics only, against state-of-the-art deep GGM models that are trained on the entire adjacency matrix. The results show that graph statistics are often sufficient to build a competitive deep GGM that generates realistic graphs while protecting local privacy.

We describe a new setting for learning a deep graph generative model (GGM) from aggregate graph statistics, rather than from the graph adjacency matrix.

We describe a new setting for learning a deep graph generative model (GGM) from aggregate graph statistics, rather than from the graph adjacency matrix. Matching the statistics of observed training graphs is the main approach for learning traditional GGMs (e.g, BTER, Chung-Lu, and Erdos-Renyi models). Privacy researchers have proposed learning from graph statistics as a way to protect privacy. We develop an architecture for training a deep GGM to match statistics while preserving local differential privacy guarantees. Empirical evaluation on 8 datasets indicates that our deep GGM model generates more realistic graphs than the traditional GGMs when both are learned from graph statistics only.

Graph learning methods help utilize implicit relationships among data items, thereby reducing training label requirements and improving task performance. However, determining the optimal graph structure for a particular learning task remains a challenging research problem. In this work, we introduce the Graph Lottery Ticket (GLT) Hypothesis - that there is an extremely sparse backbone for every graph, and that graph learning algorithms attain comparable performance when trained on that subgraph as on the full graph. We identify and systematically study 8 key metrics of interest that directly influence the performance of graph learning algorithms. Subsequently, we define the notion of a "winning ticket" for graph structure - an extremely sparse subset of edges that can deliver a robust approximation of the entire graph's performance. We propose a straightforward and efficient algorithm for finding these GLTs in arbitrary graphs. Empirically, we observe that performance of different graph learning algorithms can be matched or even exceeded on graphs with the average degree as low as 5.

Recently developed deep neural models like NetGAN, CELL, and Variational Graph Autoencoders have made progress but face limitations in replicating key graph statistics on generating large graphs. Diffusion-based methods have emerged as promising alternatives, however, most of them present challenges in computational efficiency and generative performance. EDGE is effective at modeling large networks, but its current denoising approach can be inefficient, often leading to wasted computational resources and potential mismatches in its generation process. In this paper, we propose enhancements to the EDGE model to address these issues. Specifically, we introduce a degree-specific noise schedule that optimizes the number of active nodes at each timestep, significantly reducing memory consumption. Additionally, we present an improved sampling scheme that fine-tunes the generative process, allowing for better control over the similarity between the synthesized and the true network. Our experimental results demonstrate that the proposed modifications not only improve the efficiency but also enhance the accuracy of the generated graphs, offering a robust and scalable solution for graph generation tasks.

Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in other applications such as tabular and graph data generation. However, due to computational complexity, to this date, the application of these techniques to graph data has been restricted to small 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 by augmenting a diffusion model (DiGress) with a generalized divide-and-conquer framework. The algorithm is capable of generating larger graphs by sampling a covering of subgraphs of the initial graph in order to train DiGress. SaGess then constructs a synthetic graph using the subgraphs that have been generated by DiGress. 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.

We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of drawing large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common "hairball" look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.