This paper challenges the convention of using graph-theoretic shortest distance in stress-based graph drawing. We propose a new paradigm based on resistance distance, derived from the graph Laplacian's spectrum, which better captures global graph structure. This approach overcomes theoretical and computational limitations of traditional methods, as resistance distance admits a natural isometric embedding in Euclidean space. Our experiments demonstrate improved neighborhood preservation and cluster faithfulness. We introduce Omega, a linear-time graph drawing algorithm that integrates a fast resistance distance embedding with random node-pair sampling for Stochastic Gradient Descent (SGD). This comprehensive random sampling strategy, enabled by efficient pre-computation of resistance distance embeddings, is more effective and robust than pivot-based sampling used in prior algorithms, consistently achieving lower and more stable stress values. The algorithm maintains $O(|E|)$ complexity for both weighted and unweighted graphs. Our work establishes a connection between spectral graph theory and stress-based layouts, providing a practical and scalable solution for network visualization.

翻译：本文对基于应力的图绘制中采用图论最短距离的传统做法提出挑战。我们提出了一种基于电阻距离的新范式，该距离源自图拉普拉斯算子的谱特性，能更好地捕捉图的全局结构。此方法克服了传统方法的理论与计算局限，因为电阻距离允许在欧几里得空间中实现自然的等距嵌入。实验结果表明，该方法在邻域保持和簇结构保真度方面均有提升。我们提出了Omega算法，这是一种线性时间复杂度的图绘制算法，将快速电阻距离嵌入与随机节点对采样相结合以进行随机梯度下降。这种全面的随机采样策略得益于电阻距离嵌入的高效预计算，相比先前算法中基于枢轴的采样方法更为有效和鲁棒，能够持续获得更低且更稳定的应力值。该算法对加权图和非加权图均保持$O(|E|)$的时间复杂度。本研究建立了谱图理论与基于应力的布局之间的联系，为网络可视化提供了实用且可扩展的解决方案。