We consider the problem of generating private synthetic versions of real-world graphs containing private information while maintaining the utility of generated graphs. Differential privacy is a gold standard for data privacy, and the introduction of the differentially private stochastic gradient descent (DP-SGD) algorithm has facilitated the training of private neural models in a number of domains. Recent advances in graph generation via deep generative networks have produced several high performing models. We evaluate and compare state-of-the-art models including adjacency matrix based models and edge based models, and show a practical implementation that favours the edge-list approach utilizing the Gaussian noise mechanism when evaluated on commonly used graph datasets. Based on our findings, we propose a generative model that can reproduce the properties of real-world networks while maintaining edge-differential privacy. The proposed model is based on a stochastic neural network that generates discrete edge-list samples and is trained using the Wasserstein GAN objective with the DP-SGD optimizer. Being the first approach to combine these beneficial properties, our model contributes to further research on graph data privacy.
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