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Connectivity-Faithful Graph Drawing

Authors Amyra Meidiana , Seok-Hee Hong , Yongcheng Jing

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ACM Subject Classification
  • Human-centered computing → Graph drawings
Keywords
  • Graph connectivity
  • Faithful graph drawing
  • Graph sparsification

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Abstract

Connectivity is one of the important fundamental structural properties of graphs, and a graph drawing D should faithfully represent the connectivity structure of the underlying graph G. This paper investigates connectivity-faithful graph drawing leveraging the famous Nagamochi-Ibaraki (NI) algorithm, which computes a sparsification G_NI, preserving the k-connectivity of a k-connected graph G. 
Specifically, we first present CFNI, a divide-and-conquer algorithm, which computes a sparsification G_CFNI, which preserves the global k-connectivity of a graph G and the local h-connectivity of the h-connected components of G. We then present CFGD, a connectivity-faithful graph drawing algorithm based on CFNI, which faithfully displays the global and local connectivity structure of G. Extensive experiments demonstrate that CFNI outperforms NI with 66% improvement in the connectivity-related sampling quality metrics and 73% improvement in proxy quality metrics. Consequently, CFGD outperforms a naive application of NI for graph drawing, in particular with 62% improvement in stress metrics. Moreover, CFGD runs 51% faster than drawing the whole graph G, with a similar quality.

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Amyra Meidiana, Seok-Hee Hong, and Yongcheng Jing. Connectivity-Faithful Graph Drawing. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.17

Author Details

Amyra Meidiana
  • University of Sydney, Australia
Seok-Hee Hong
  • University of Sydney, Australia
Yongcheng Jing
  • University of Sydney, Australia

Funding

This work was funded by ARC (Australian Research Council) DP (Discovery Project) grant DP190103301.

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