Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path distance. However, stress optimization presents computational challenges due to its inherent complexity and is usually solved using heuristics in practice. We introduce a scalable Graph Neural Network (GNN) based Graph Drawing framework with sub-quadratic runtime that can learn to optimize stress. Inspired by classical stress optimization techniques and force-directed layout algorithms, we create a coarsening hierarchy for the input graph. Beginning at the coarsest level, we iteratively refine and un-coarsen the layout, until we generate an embedding for the original graph. To enhance information propagation within the network, we propose a novel positional rewiring technique based on intermediate node positions. Our empirical evaluation demonstrates that the framework achieves state-of-the-art performance while remaining scalable.

翻译：图可视化（亦称图绘制）旨在寻找满足特定优化准则的几何嵌入。应力是广泛使用的度量指标，当所有节点对均被置于其最短路径距离时应力最小。然而，应力优化因其固有复杂性面临计算挑战，实际应用中通常采用启发式方法求解。我们提出一种基于图神经网络（GNN）的可扩展图绘制框架，该框架具有次二次方时间复杂度且可学习优化应力。受经典应力优化技术与力导向布局算法启发，我们为输入图构建多级粗化层次结构。从最粗层次开始，迭代细化并反粗化布局，最终生成原始图的嵌入表示。为增强网络内信息传播，我们提出一种基于中间节点位置的新型位置重连技术。实证评估表明，该框架在保持可扩展性的同时实现了最优性能。