Training on large-scale graphs has achieved remarkable results in graph representation learning, but its cost and storage have attracted increasing concerns. Existing graph condensation methods primarily focus on optimizing the feature matrices of condensed graphs while overlooking the impact of the structure information from the original graphs. To investigate the impact of the structure information, we conduct analysis from the spectral domain and empirically identify substantial Laplacian Energy Distribution (LED) shifts in previous works. Such shifts lead to poor performance in cross-architecture generalization and specific tasks, including anomaly detection and link prediction. In this paper, we propose a novel Structure-broadcasting Graph Dataset Distillation (SGDD) scheme for broadcasting the original structure information to the generation of the synthetic one, which explicitly prevents overlooking the original structure information. Theoretically, the synthetic graphs by SGDD are expected to have smaller LED shifts than previous works, leading to superior performance in both cross-architecture settings and specific tasks. We validate the proposed SGDD across 9 datasets and achieve state-of-the-art results on all of them: for example, on the YelpChi dataset, our approach maintains 98.6% test accuracy of training on the original graph dataset with 1,000 times saving on the scale of the graph. Moreover, we empirically evaluate there exist 17.6% ~ 31.4% reductions in LED shift crossing 9 datasets. Extensive experiments and analysis verify the effectiveness and necessity of the proposed designs. The code is available in the GitHub repository: https://github.com/RingBDStack/SGDD.

翻译：在大规模图上进行训练在图表征学习中取得了显著成果，但其成本和存储问题日益引起关注。现有的图浓缩方法主要侧重于优化浓缩图的特征矩阵，而忽视了原始图结构信息的影响。为探究结构信息的影响，我们从谱域角度进行分析，并经验性地发现先前工作中存在显著的拉普拉斯能量分布（LED）偏移。这种偏移导致跨架构泛化性能下降，以及异常检测和链路预测等特定任务效果不佳。本文提出一种新颖的结构广播图数据集蒸馏（SGDD）方案，将原始结构信息广播到合成图的生成过程中，明确防止对原始结构信息的忽视。理论上，相较于先前工作，SGDD生成的合成图预期具有更小的LED偏移，从而在跨架构设置和特定任务中均展现出优越性能。我们在9个数据集上验证了所提SGDD方法，并在所有数据集上取得了最先进的结果：例如，在YelpChi数据集上，我们的方法在保持原始图数据集训练测试准确率98.6%的同时，将图的规模节省了1000倍。此外，我们经验性地评估了9个数据集的LED偏移减少了17.6%~31.4%。大量实验与分析验证了所提设计的有效性与必要性。代码已开源至GitHub仓库：https://github.com/RingBDStack/SGDD。