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Author Xu, Taihua ♦ Yang, Jie ♦ Gou, Guanglei
Editor Hitzer, Eckhard
Source Hindawi
Content type Text
Publisher Hindawi
File Format PDF
Copyright Year ©2018
Language English
Abstract Symmetry is one of the most important aesthetic criteria on graph drawing. It is quite necessary to measure the extent to which the drawings can be considered symmetric. For this purpose, a symmetric metric based on vertex coordinate calculation is proposed in this paper. It is proven theoretically and experimentally that the proposed metric is robust to contraction, expansion, and rotation of drawings. This robustness conforms to human perception of symmetry. Star-subgraphs and cycles are two common structures in digraphs. Both of them have inherent symmetry which should be displayed in drawings. For this purpose, a force-directed algorithm named FDS is proposed which can draw star-subgraphs and cycles as symmetrically as possible. FDS algorithm draws cycles as circles whose positions are fixed to provide a scaffolding for overall layout, renders non-leaf vertices by a standard force-directed layout, and places leaf vertices on concentric circles via a deterministic strategy. A series of experiments are carried out to test FDS algorithm. The results show that FDS algorithm draws digraphs more symmetrically than the existing state-of-the-art algorithms and performs efficiency comparable to O(nlog⁡n) YFHu algorithm.
ISSN 1024123X
Learning Resource Type Article
Publisher Date 2018-11-19
Rights License This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
e-ISSN 15635147
Journal Mathematical Problems in Engineering
Volume Number 2018
Page Count 24


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