Fast and Faithful Edge Bundling using Spectral Sparsification

2026-04-28

AI Summary

Existing edge bundling methods often introduce visual distortion and topological ambiguity due to high computational complexity. This work proposes a novel spectral sparsification–based paradigm for edge bundling: it first introduces effective resistance as an innovative measure of edge compatibility to construct SEB, a spectrally faithful edge bundling method; then develops FEB, a general-purpose acceleration framework that substantially reduces computational overhead while preserving structural fidelity. A complementary evaluation framework, FBQ, is also introduced to quantitatively assess visualization quality. Experimental results demonstrate that SEB improves distortion and ambiguity metrics by 46% and 17% on average, respectively, while FEB reduces runtime by 61% with a structural fidelity of 74%.

Abstract

Edge bundling reduces the visual complexity of drawings of large and complex graphs by clustering "compatible" edges. However, it often introduces distortion by bundling "unrelated" edges, resulting in misleading, ambiguous drawings. Moreover, existing edge bundling methods often have high computational complexity. We present new edge bundling methods and faithfulness metrics for edge bundling using spectral sparsification, which sparsifies a graph G into a subgraph G' with O(n log n) edges, based on the effective resistance values of edges, preserving the spectrum of G, closely related to important structural properties of G, such as connectivity, clustering, and the commute distance. We first present a new edge bundling method SEB (Spectral Edge Bundling), introducing effective resistance-based compatibility for spectral-faithful bundling, improving distortion and ambiguity. Then, we present a general framework FEB (Fast Edge Bundling) utilizing spectral sparsification to improve the efficiency of existing bundling methods while maintaining a similar quality. We also present FBQ (Fast Bundling Quality) framework for proxy bundle faithfulness metrics, for measuring how FEB faithfully preserves the ground truth structure in the original edge bundling, with two variants, FBQ_JS (utilizing Jaccard Similarity) and FBQ_SQ (utilizing sampling quality metrics). Extensive experiments using various real-world and synthetic graphs demonstrate the effectiveness of SEB for edge bundling, outperforming state-of-art bundling methods on quality metrics, with 46% and 17% average improvement in distortion and ambiguity respectively for SEB2. Furthermore, experiments successfully demonstrate the efficiency of the FEB framework, with 61% runtime improvement over the original edge bundling methods without sparsification, while maintaining a similar quality, with 74% similarity based on FBQ_SQ.

Problem

• edge bundling
• visual distortion
• computational complexity
• graph visualization
• faithfulness

Innovation

• spectral sparsification
• edge bundling
• effective resistance
• faithfulness metrics
• graph visualization