Although powerful graph neural networks (GNNs) have boosted numerous real-world applications, the potential privacy risk is still underexplored. To close this gap, we perform the first comprehensive study of graph reconstruction attack that aims to reconstruct the adjacency of nodes. We show that a range of factors in GNNs can lead to the surprising leakage of private links. Especially by taking GNNs as a Markov chain and attacking GNNs via a flexible chain approximation, we systematically explore the underneath principles of graph reconstruction attack, and propose two information theory-guided mechanisms: (1) the chain-based attack method with adaptive designs for extracting more private information; (2) the chain-based defense method that sharply reduces the attack fidelity with moderate accuracy loss. Such two objectives disclose a critical belief that to recover better in attack, you must extract more multi-aspect knowledge from the trained GNN; while to learn safer for defense, you must forget more link-sensitive information in training GNNs. Empirically, we achieve state-of-the-art results on six datasets and three common GNNs. The code is publicly available at: https://github.com/tmlr-group/MC-GRA.

In this paper, we measure the privacy leakage via studying whether graph representations can be inverted to recover the graph used to generate them via graph reconstruction attack (GRA). We propose a GRA that recovers a graph's adjacency matrix from the representations via a graph decoder that minimizes the reconstruction loss between the partial graph and the reconstructed graph. We study three types of representations that are trained on the graph, i.e., representations output from graph convolutional network (GCN), graph attention network (GAT), and our proposed simplicial neural network (SNN) via a higher-order combinatorial Laplacian. Unlike the first two types of representations that only encode pairwise relationships, the third type of representation, i.e., SNN outputs, encodes higher-order interactions (e.g., homological features) between nodes. We find that the SNN outputs reveal the lowest privacy-preserving ability to defend the GRA, followed by those of GATs and GCNs, which indicates the importance of building more private representations with higher-order node information that could defend the potential threats, such as GRAs.

Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph analytics problem by transforming the graph data into low-dimensional vectors. These vectors could also be shared with third parties to gain additional insights of what is behind the data. While sharing graph embedding is intriguing, the associated privacy risks are unexplored. In this paper, we systematically investigate the information leakage of the graph embedding by mounting three inference attacks. First, we can successfully infer basic graph properties, such as the number of nodes, the number of edges, and graph density, of the target graph with up to 0.89 accuracy. Second, given a subgraph of interest and the graph embedding, we can determine with high confidence that whether the subgraph is contained in the target graph. For instance, we achieve 0.98 attack AUC on the DD dataset. Third, we propose a novel graph reconstruction attack that can reconstruct a graph that has similar graph structural statistics to the target graph. We further propose an effective defense mechanism based on graph embedding perturbation to mitigate the inference attacks without noticeable performance degradation for graph classification tasks. Our code is available at https://github.com/Zhangzhk0819/GNN-Embedding-Leaks.