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A Force-Directed Algorithm for Drawing Directed Graphs Symmetrically

机译：对称绘制有向图的力导向算法

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摘要

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(n log n) YFHu algorithm.
机译：对称性是图形绘制中最重要的美学标准之一。非常有必要测量可以认为附图对称的程度。为此，本文提出了一种基于顶点坐标计算的对称度量。从理论上和实验上都证明，所提出的度量标准对图纸的收缩，扩展和旋转具有鲁棒性。这种鲁棒性符合人类对对称性的感知。星图和周期图是有向图的两个常见结构。两者都有固有的对称性，应在图纸中显示。为此，提出了一种称为FDS的力导向算法，该算法可以尽可能对称地绘制星形图和周期图。 FDS算法将循环绘制为固定位置的圆形，以提供整体布局的脚手架，通过标准的力导向布局渲染非叶顶点，并通过确定性策略将叶顶点放置在同心圆上。进行了一系列实验以测试FDS算法。结果表明，FDS算法比现有的最新算法更对称地绘制图，并且其效率可与O（n log n）YFHu算法媲美。

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  • 来源
    《Mathematical Problems in Engineering》 |2018年第15期|6208509.1-6208509.24|共24页
  • 作者

    Xu Taihua; Yang Jie; Gou Guanglei;

  • 作者单位

    Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu 610031 Sichuan Peoples R China|Chongqing Univ Posts & Telecommun Chongqing Key Lab Computat Intelligence Chongqing 400065 Peoples R China;

    Chongqing Univ Posts & Telecommun Chongqing Key Lab Computat Intelligence Chongqing 400065 Peoples R China|Zunyi Normal Univ Sch Phys & Elect Sci Zunyi 563002 Peoples R China;

    Chongqing Univ Technol Sch Comp Sci & Engn Chongqing 400054 Peoples R China;

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