Federated Graph Condensation with Information Bottleneck Principles

Graph condensation, which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has immediately benefited various graph learning tasks. However, existing graph condensation methods rely on centralized data storage, which is unfeasible for real-world decentralized data distribution, and overlook data holders' privacy-preserving requirements. To bridge the gap, we propose and study the novel problem of federated graph condensation for graph neural networks (GNNs). Specifically, we first propose a general framework for federated graph condensation, in which we decouple the typical gradient matching process for graph condensation into client-side gradient calculation and server-side gradient matching. In this way, the burdensome computation cost in client-side is largely alleviated. Besides, our empirical studies show that under the federated setting, the condensed graph will consistently leak data membership privacy, i.e., the condensed graph during the federated training can be utilized to steal the training data under the membership inference attacks (MIA). To tackle this issue, we innovatively incorporate information bottleneck principles into the federated graph condensation, which only needs to extract partial node features in one local pre-training step and utilize the features during federated training. Extensive experiments on real-world datasets demonstrate that our framework can consistently protect membership privacy during training. Meanwhile, it also achieves comparable and even superior performance against existing centralized graph condensation and federated graph learning methods.