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1. Virtual Nodes Can Help: Tackling Distribution Shifts in Federated Graph Learning

   https://doi.org/10.1609/aaai.v39i16.33830  

   Fu, Xingbo; Chen, Zihan; He, Yinhan; Wang, Song; Zhang, Binchi; Chen, Chen; Li, Jundong (April 2025, Proceedings of the AAAI Conference on Artificial Intelligence)

   Federated Graph Learning (FGL) enables multiple clients to jointly train powerful graph learning models, e.g., Graph Neural Networks (GNNs), without sharing their local graph data for graph-related downstream tasks, such as graph property prediction. In the real world, however, the graph data can suffer from significant distribution shifts across clients as the clients may collect their graph data for different purposes. In particular, graph properties are usually associated with invariant label-relevant substructures (i.e., subgraphs) across clients, while label-irrelevant substructures can appear in a client-specific manner. The issue of distribution shifts of graph data hinders the efficiency of GNN training and leads to serious performance degradation in FGL. To tackle the aforementioned issue, we propose a novel FGL framework entitled FedVN that eliminates distribution shifts through client-specific graph augmentation strategies with multiple learnable Virtual Nodes (VNs). Specifically, FedVN lets the clients jointly learn a set of shared VNs while training a global GNN model. To eliminate distribution shifts, each client trains a personalized edge generator that determines how the VNs connect local graphs in a client-specific manner. Furthermore, we provide theoretical analyses indicating that FedVN can eliminate distribution shifts of graph data across clients. Comprehensive experiments on four datasets under five settings demonstrate the superiority of our proposed FedVN over nine baselines. 

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2. Federated Graph Classification over Non-IID Graphs

   Xie, Han; Ma, Jing; Xiong, Li; Yang, Carl (January 2021, Advances in neural information processing systems)

   Federated learning has emerged as an important paradigm for training machine learning models in different domains. For graph-level tasks such as graph classification, graphs can also be regarded as a special type of data samples, which can be collected and stored in separate local systems. Similar to other domains, multiple local systems, each holding a small set of graphs, may benefit from collaboratively training a powerful graph mining model, such as the popular graph neural networks (GNNs). To provide more motivation towards such endeavors, we analyze real-world graphs from different domains to confirm that they indeed share certain graph properties that are statistically significant compared with random graphs. However, we also find that different sets of graphs, even from the same domain or same dataset, are non-IID regarding both graph structures and node features. To handle this, we propose a graph clustered federated learning (GCFL) framework that dynamically finds clusters of local systems based on the gradients of GNNs, and theoretically justify that such clusters can reduce the structure and feature heterogeneity among graphs owned by the local systems. Moreover, we observe the gradients of GNNs to be rather fluctuating in GCFL which impedes high-quality clustering, and design a gradient sequence-based clustering mechanism based on dynamic time warping (GCFL+). Extensive experimental results and in-depth analysis demonstrate the effectiveness of our proposed frameworks. 

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3. Supervised Community Detection with Line Graph Neural Networks

   Chen, Zhengdao; Li, Lisha; Bruna, Joan (May 2019, International Conference on Learning Representations)

   Community detection in graphs can be solved via spectral methods or posterior inference under certain probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thresholds in terms of the signal-to-noise ratio. By recasting community detection as a node-wise classification problem on graphs, we can also study it from a learning perspective. We present a novel family of Graph Neural Networks (GNNs) for solving community detection problems in a supervised learning setting. We show that, in a data-driven manner and without access to the underlying generative models, they can match or even surpass the performance of the belief propagation algorithm on binary and multiclass stochastic block models, which is believed to reach the computational threshold in these cases. In particular, we propose to augment GNNs with the non-backtracking operator defined on the line graph of edge adjacencies. The GNNs are achieved good performance on real-world datasets. In addition, we perform the first analysis of the optimization landscape of using (linear) GNNs to solve community detection problems, demonstrating that under certain simplifications and assumptions, the loss value at any local minimum is close to the loss value at the global minimum/minima. 

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4. Supervised Community Detection with Line Graph Neural Networks

   Chen, Zhengdao; Li, Lisha; Bruna, Joan (May 2020, International conference on learning representations)

   Community detection in graphs can be solved via spectral methods or posterior inference under certain probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thresholds in terms of the signal-to-noise ratio. By recasting community detection as a node-wise classification problem on graphs, we can also study it from a learning perspective. We present a novel family of Graph Neural Networks (GNNs) for solving community detection problems in a supervised learning setting. We show that, in a data-driven manner and without access to the underlying generative models, they can match or even surpass the performance of the belief propagation algorithm on binary and multiclass stochastic block models, which is believed to reach the computational threshold in these cases. In particular, we propose to augment GNNs with the non-backtracking operator defined on the line graph of edge adjacencies. The GNNs are achieved good performance on real-world datasets. In addition, we perform the first analysis of the optimization landscape of using (linear) GNNs to solve community detection problems, demonstrating that under certain simplifications and assumptions, the loss value at any local minimum is close to the loss value at the global minimum/minima. 

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5. Graph mixup with soft alignments

   Hongyi Ling, Zhimeng Jiang (July 2023, ICML2023)

   We study graph data augmentation by mixup, which has been used successfully on images. A key operation of mixup is to compute a convex combination of a pair of inputs. This operation is straightforward for grid-like data, such as images, but challenging for graph data. The key difficulty lies in the fact that different graphs typically have different numbers of nodes, and thus there lacks a node-level correspondence between graphs. In this work, we propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments. Specifically, given a pair of graphs, we explicitly obtain node-level correspondence via computing a soft assignment matrix to match the nodes between two graphs. Based on the soft assignments, we transform the adjacency and node feature matrices of one graph, so that the transformed graph is aligned with the other graph. In this way, any pair of graphs can be mixed directly to generate an augmented graph. We conduct systematic experiments to show that S-Mixup can improve the performance and generalization of graph neural networks (GNNs) on various graph classification tasks. In addition, we show that S-Mixup can increase the robustness of GNNs against noisy labels. Our code is publicly available as part of the DIG package (https://github.com/divelab/DIG). 

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