Signed graphs with positive and negative edges can model complex relationships in social networks. Leveraging on balance theory that deduces edge signs from multi-hop node pairs, signed graph learning can generate node embeddings that preserve both structural and sign information. However, training on sensitive signed graphs raises significant privacy concerns, as model parameters may leak private link information. Existing methods with differential privacy (DP) typically rely on edge or gradient perturbation for protecting unsigned graphs. Yet, they are not well-suited for signed graphs: edge perturbation may trigger cascading errors in edge sign inference under balance theory, while gradient perturbation necessitates substantial noise injection due to increased gradient sensitivity arising from node interdependence and gradient polarity change caused by sign flips. In this paper, motivated by the robustness of adversarial learning to noisy interactions, we present ASGL, a privacy-preserving adversarial signed graph learning method that preserves high utility while achieving node-level DP. We first decompose signed graphs into positive and negative subgraphs based on edge signs, and then design a gradient-perturbed adversarial module to approximate the true signed connectivity distribution. In particular, the gradient perturbation helps mitigate cascading errors, while the subgraph separation facilitates sensitivity reduction. Further, we devise a constrained breadth-first search tree strategy that fuses with balance theory to identify the edge signs between generated node pairs. This strategy also enables gradient decoupling, thereby effectively lowering gradient sensitivity. Extensive experiments on real-world datasets show that ASGL achieves favorable privacy-utility trade-offs across multiple downstream tasks.

Influence Maximization (IM), aiming to identify a small set of highly influential nodes in social networks, is a critical problem in graph analysis. Recently, Graph Neural Networks (GNNs) have demonstrated superior effectiveness in addressing IM. However, a trained GNN still raises significant privacy concerns, as it may expose sensitive node features and structural information. While Differential Privacy (DP) techniques have been widely applied to GNNs for node-level tasks, they cannot be directly extended to 1M problems. This is because IM requires more complex structural information for training, resulting in an extremely larger DP noise scale than node-level tasks. To tackle these issues, we propose PrivIM, a novel differentially private subgraph-based GNNs framework for IM tasks, which ensures node-level DP guarantees. Within PrivIM, we design a unique dual-stage adaptive frequency sampling scheme to optimize the model utility. First, it reduces the correlation between nodes by dynamically adjusting each node's sampling probability. Then additional subgraphs are incorporated to supplement boundary structural information, enhancing utility without increasing privacy budget. Extensive experiments on six real-world datasets demonstrate that PrivIM maintains high utility in IM compared to baseline methods.

Graph embedding generation techniques aim to learn low-dimensional vectors for each node in a graph and have recently gained increasing research attention. Publishing low-dimensional node vectors enables various graph analysis tasks, such as structural equivalence and link prediction. Yet, improper publication opens a backdoor to malicious attackers, who can infer sensitive information of individuals from the low-dimensional node vectors. Existing methods tackle this issue by developing deep graph learning models with differential privacy (DP). However, they often suffer from large noise injections and cannot provide structural preferences consistent with mining objectives. Recently, skip-gram based graph embedding generation techniques are widely used due to their ability to extract customizable structures. Based on skip-gram, we present SE-PrivGEmb, a structure-preference enabled graph embedding generation under DP. For arbitrary structure preferences, we design a unified noise tolerance mechanism via perturbing non-zero vectors. This mechanism mitigates utility degradation caused by high sensitivity. By carefully designing negative sampling probabilities in skip-gram, we theoretically demonstrate that skip-gram can preserve arbitrary proximities, which quantify structural features in graphs. Extensive experiments show that our method outperforms existing state-of-the-art methods under structural equivalence and link prediction tasks.

The skip-gram model (SGM), which employs a neural network to generate node vectors, serves as the basis for numerous popular graph embedding techniques. However, since the training datasets contain sensitive linkage information, the parameters of a released SGM may encode private information and pose significant privacy risks. Differential privacy (DP) is a rigorous standard for protecting individual privacy in data analysis. Nevertheless, when applying differential privacy to skip-gram in graphs, it becomes highly challenging due to the complex link relationships, which potentially result in high sensitivity and necessitate substantial noise injection. To tackle this challenge, we present AdvSGM, a differentially private skip-gram for graphs via adversarial training. Our core idea is to leverage adversarial training to privatize skip-gram while improving its utility. Towards this end, we develop a novel adversarial training module by devising two optimizable noise terms that correspond to the parameters of a skip-gram. By fine-tuning the weights between modules within AdvSGM, we can achieve differentially private gradient updates without additional noise injection. Extensive experimental results on six real-world graph datasets show that AdvSGM preserves high data utility across different downstream tasks.

The objective of privacy-preserving synthetic graph publishing is to safeguard individuals' privacy while retaining the utility of original data. Most existing methods focus on graph neural networks under differential privacy (DP), and yet two fundamental problems in generating synthetic graphs remain open. First, the current research often encounters high sensitivity due to the intricate relationships between nodes in a graph. Second, DP is usually achieved through advanced composition mechanisms that tend to converge prematurely when working with a small privacy budget. In this paper, inspired by the simplicity, effectiveness, and ease of analysis of PageRank, we design PrivDPR, a novel privacy-preserving deep PageRank for graph synthesis. In particular, we achieve DP by adding noise to the gradient for a specific weight during learning. Utilizing weight normalization as a bridge, we theoretically reveal that increasing the number of layers in PrivDPR can effectively mitigate the high sensitivity and privacy budget splitting. Through formal privacy analysis, we prove that the synthetic graph generated by PrivDPR satisfies node-level DP. Experiments on real-world graph datasets show that PrivDPR preserves high data utility across multiple graph structural properties.

The goal of privacy-preserving social graph publishing is to protect individual privacy while preserving data utility. Community structure, which is an important global pattern of nodes, is a crucial data utility as it serves as fundamental operations for many graph analysis tasks. Yet, most existing methods with differential privacy (DP) commonly fall in edge-DP to sacrifice security in exchange for utility. Moreover, they reconstruct graphs from the local feature-extraction of nodes, resulting in poor community preservation. Motivated by this, we propose PrivCom, a strict node-DP graph publishing algorithm to maximize the utility on the community structure while maintaining a higher level of privacy. Specifically, to reduce the huge sensitivity, we devise a Katz index-based private graph feature extraction method, which can capture global graph structure features while greatly reducing the global sensitivity via a sensitivity regulation strategy. Yet, with a fixed sensitivity, the feature captured by Katz index, which is presented in matrix form, requires privacy budget splits. As a result, plenty of noise is injected, thereby mitigating global structural utility. To this end, we design a private Oja algorithm approximating eigen-decomposition, which yields the noisy Katz matrix via privately estimating eigenvectors and eigenvalues from extracted low-dimensional vectors. Experimental results confirm our theoretical findings and the efficacy of PrivCom.