“图的绘制 Graph drawing”的版本间的差异

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2020年5月12日 (二) 19:07的版本

此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。

25px  此article介紹的是the general subject of graph drawing。For the annual research symposium, see International Symposium on Graph Drawing.
Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks.

Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks.

WWW，演示超链接的一个微小部分的图形表示

Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.[1]

Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.

图形绘制是数学和计算机科学的一个领域，它结合了几何图形理论和信息可视化学的方法，从而得到来自社会网络分析、制图学、语言学和生物信息学等应用的图形的二维描述。


A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph.[2] In the abstract, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the arrangement of these vertices and edges within a drawing affects its understandability, usability, fabrication cost, and aesthetics.[3] The problem gets worse if the graph changes over time by adding and deleting edges (dynamic graph drawing) and the goal is to preserve the user's mental map.[4]

A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph. In the abstract, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the arrangement of these vertices and edges within a drawing affects its understandability, usability, fabrication cost, and aesthetics.

图形或网络图的绘制是图形的顶点和边的图形表示。这个图形不应与图形本身混淆: 非常不同的布局可以对应于同一个图形。抽象地说，重要的是哪一对顶点是由边连接的。然而，在具体的绘图中，这些顶点和边的排列影响了它的可理解性、可用性、制造成本和美学。


Graphical conventions

Directed graph with arrowheads showing edge directions

Directed graph with arrowheads showing edge directions

[带箭头显示边方向的有向图]

Graphs are frequently drawn as node–link diagrams in which the vertices are represented as disks, boxes, or textual labels and the edges are represented as line segments, polylines, or curves in the Euclidean plane.[3] Node–link diagrams can be traced back to the 13th century work of Ramon Llull, who drew diagrams of this type for complete graphs in order to analyze all pairwise combinations among sets of metaphysical concepts.[5]

Graphs are frequently drawn as node–link diagrams in which the vertices are represented as disks, boxes, or textual labels and the edges are represented as line segments, polylines, or curves in the Euclidean plane. Node–link diagrams can be traced back to the 13th century work of Ramon Llull, who drew diagrams of this type for complete graphs in order to analyze all pairwise combinations among sets of metaphysical concepts.

图经常绘制成节点链接图，其中顶点表示为圆盘、框或文本标签，边表示为欧几里德平面上的线段、折线或曲线。节点链接图可以追溯到13世纪雷蒙 · 卢尔的作品，他为完全图绘制了这种类型的图，以便分析形而上学概念集合之间的所有成对组合。


In the case of directed graphs, arrowheads form a commonly used graphical convention to show their orientation;[2] however, user studies have shown that other conventions such as tapering provide this information more effectively.[6] Upward planar drawing uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.[7]

In the case of directed graphs, arrowheads form a commonly used graphical convention to show their orientation; Upward planar drawing uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.

在有向图的情况下，箭头形成一个常用的图形约定来显示它们的方向; 向上平面绘图使用的约定是每条边从一个较低的顶点定向到一个较高的顶点，使箭头没有必要。


Alternative conventions to node–link diagrams include adjacency representations such as circle packings, in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; intersection representations in which vertices are represented by non-disjoint geometric objects and edges are represented by their intersections; visibility representations in which vertices are represented by regions in the plane and edges are represented by regions that have an unobstructed line of sight to each other; confluent drawings, in which edges are represented as smooth curves within mathematical train tracks; fabrics, in which nodes are represented as horizontal lines and edges as vertical lines;[8] and visualizations of the adjacency matrix of the graph.

Alternative conventions to node–link diagrams include adjacency representations such as circle packings, in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; intersection representations in which vertices are represented by non-disjoint geometric objects and edges are represented by their intersections; visibility representations in which vertices are represented by regions in the plane and edges are represented by regions that have an unobstructed line of sight to each other; confluent drawings, in which edges are represented as smooth curves within mathematical train tracks; fabrics, in which nodes are represented as horizontal lines and edges as vertical lines; and visualizations of the adjacency matrix of the graph.

节点链接图的替代约定包括邻接表示，如圆填充，其中顶点表示为平面上不相交的区域，边表示为区域之间的邻接; 交叉表示，顶点表示为不相交的几何对象，边表示为它们的交点; 可见性表示，顶点表示为平面上的区域，边表示为彼此视线不受阻碍的区域; 汇流图，其中边表示为数学列车轨道上的光滑曲线; 织物，其中顶点表示为水平线，边表示为垂直线; 以及图形邻接矩阵的可视化结点。


Quality measures

Many different quality measures have been defined for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability.[9] In addition to guiding the choice between different layout methods for the same graph, some layout methods attempt to directly optimize these measures.

Many different quality measures have been defined for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability. In addition to guiding the choice between different layout methods for the same graph, some layout methods attempt to directly optimize these measures.

为了找到客观评价图形美观性和可用性的方法，已经定义了许多不同的图形质量度量。除了指导同一图形在不同布局方法之间的选择外，一些布局方法试图直接优化这些措施。

Planar graph drawn without overlapping edges

Planar graph drawn without overlapping edges

没有重叠边的平面图

  • The crossing number of a drawing is the number of pairs of edges that cross each other. If the graph is planar, then it is often convenient to draw it without any edge intersections; that is, in this case, a graph drawing represents a graph embedding. However, nonplanar graphs frequently arise in applications, so graph drawing algorithms must generally allow for edge crossings.[10]
  • The area of a drawing is the size of its smallest bounding box, relative to the closest distance between any two vertices. Drawings with smaller area are generally preferable to those with larger area, because they allow the features of the drawing to be shown at greater size and therefore more legibly. The aspect ratio of the bounding box may also be important.
  • Symmetry display is the problem of finding symmetry groups within a given graph, and finding a drawing that displays as much of the symmetry as possible. Some layout methods automatically lead to symmetric drawings; alternatively, some drawing methods start by finding symmetries in the input graph and using them to construct a drawing.[11]
  • It is important that edges have shapes that are as simple as possible, to make it easier for the eye to follow them. In polyline drawings, the complexity of an edge may be measured by its number of bends, and many methods aim to provide drawings with few total bends or few bends per edge. Similarly for spline curves the complexity of an edge may be measured by the number of control points on the edge.
  • Several commonly used quality measures concern lengths of edges: it is generally desirable to minimize the total length of the edges as well as the maximum length of any edge. Additionally, it may be preferable for the lengths of edges to be uniform rather than highly varied.
  • Angular resolution is a measure of the sharpest angles in a graph drawing. If a graph has vertices with high degree then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree.[12]
  • The slope number of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (allowing crossings). Cubic graphs have slope number at most four, but graphs of degree five may have unbounded slope number; it remains open whether the slope number of degree-4 graphs is bounded.[12]


Layout methods

A force-based network visualization.[13]

There are many different graph layout strategies:

A force-based network visualization.There are many different graph layout strategies:

基于力量的网络可视化。有许多不同的图形布局策略:

  • In force-based layout systems, the graph drawing software modifies an initial vertex placement by continuously moving the vertices according to a system of forces based on physical metaphors related to systems of springs or molecular mechanics. Typically, these systems combine attractive forces between adjacent vertices with repulsive forces between all pairs of vertices, in order to seek a layout in which edge lengths are small while vertices are well-separated. These systems may perform gradient descent based minimization of an energy function, or they may translate the forces directly into velocities or accelerations for the moving vertices.[14]
  • Orthogonal layout methods, which allow the edges of the graph to run horizontally or vertically, parallel to the coordinate axes of the layout. These methods were originally designed for VLSI and PCB layout problems but they have also been adapted for graph drawing. They typically involve a multiphase approach in which an input graph is planarized by replacing crossing points by vertices, a topological embedding of the planarized graph is found, edge orientations are chosen to minimize bends, vertices are placed consistently with these orientations, and finally a layout compaction stage reduces the area of the drawing.[16]
  • Tree layout algorithms these show a rooted tree-like formation, suitable for trees. Often, in a technique called "balloon layout", the children of each node in the tree are drawn on a circle surrounding the node, with the radii of these circles diminishing at lower levels in the tree so that these circles do not overlap.[17]
  • Layered graph drawing methods (often called Sugiyama-style drawing) are best suited for directed acyclic graphs or graphs that are nearly acyclic, such as the graphs of dependencies between modules or functions in a software system. In these methods, the nodes of the graph are arranged into horizontal layers using methods such as the Coffman–Graham algorithm, in such a way that most edges go downwards from one layer to the next; after this step, the nodes within each layer are arranged in order to minimize crossings.[18]
Arc diagram

Arc diagram

弧线图

  • Arc diagrams, a layout style dating back to the 1960s,[19] place vertices on a line; edges may be drawn as semicircles above or below the line, or as smooth curves linked together from multiple semicircles.
  • Circular layout methods place the vertices of the graph on a circle, choosing carefully the ordering of the vertices around the circle to reduce crossings and place adjacent vertices close to each other. Edges may be drawn either as chords of the circle or as arcs inside or outside of the circle. In some cases, multiple circles may be used.[20]
  • Dominance drawing places vertices in such a way that one vertex is upwards, rightwards, or both of another if and only if it is reachable from the other vertex. In this way, the layout style makes the reachability relation of the graph visually apparent.[21]


Application-specific graph drawings

Graphs and graph drawings arising in other areas of application include

Graphs and graph drawings arising in other areas of application include

在其他应用领域出现的图形和图形绘图包括

  • Data-flow diagrams, drawings in which the nodes represent the components of an information system and the edges represent the movement of information from one component to another.


In addition, the placement and routing steps of electronic design automation (EDA) are similar in many ways to graph drawing, as is the problem of greedy embedding in distributed computing, and the graph drawing literature includes several results borrowed from the EDA literature. However, these problems also differ in several important ways: for instance, in EDA, area minimization and signal length are more important than aesthetics, and the routing problem in EDA may have more than two terminals per net while the analogous problem in graph drawing generally only involves pairs of vertices for each edge.

In addition, the placement and routing steps of electronic design automation (EDA) are similar in many ways to graph drawing, as is the problem of greedy embedding in distributed computing, and the graph drawing literature includes several results borrowed from the EDA literature. However, these problems also differ in several important ways: for instance, in EDA, area minimization and signal length are more important than aesthetics, and the routing problem in EDA may have more than two terminals per net while the analogous problem in graph drawing generally only involves pairs of vertices for each edge.

此外，电子设计自动化图的布局和路由步骤在许多方面与图形绘制相似，就像在分布式计算图中贪婪嵌入的问题一样，图形绘制文献包括从 EDA 文献中借用的一些结果。然而，这些问题也在几个重要方面有所不同: 例如，在 EDA，面积最小化和信号长度比美观更重要，在 EDA 的路由问题可能每个网有两个以上的终端，而图绘制中的类似问题通常只涉及每条边的顶点对。


Software

A graph drawing interface (Gephi 0.9.1)

Software, systems, and providers of systems for drawing graphs include:

A graph drawing interface (Gephi 0.9.1)Software, systems, and providers of systems for drawing graphs include:

图形绘制接口(Gephi 0.9.1)软件、系统和绘制图形系统的提供者包括:


! -- 不要在这里包含条目，除非它已经有一个带蓝色字母的文章 --

  • BioFabric open-source software for visualizing large networks by drawing nodes as horizontal lines.
  • Cytoscape, open-source software for visualizing molecular interaction networks
  • Gephi, open-source network analysis and visualization software
  • Mathematica, a general purpose computation tool that includes 2D and 3D graph visualization and graph analysis tools.[25][26]
  • NetworkX is a Python library for studying graphs and networks.
  • Tom Sawyer Software[28] Tom Sawyer Perspectives is graphics-based software for building enterprise-class graph and data visualization and analysis applications. It is a Software Development Kit (SDK) with a graphics-based design and preview environment.
  • yEd, a graph editor with graph layout functionality[30]
  • LaNet-vi, an open-source large network visualization software
  • Edraw Max 2D business technical diagramming software


References

Footnotes

Footnotes

脚注

  1. ↑ Di Battista et al. (1994), pp. vii–viii; Herman, Melançon & Marshall (2000), Section 1.1, "Typical Application Areas".
  2. ↑ 2.0 2.1 Di Battista et al. (1994), p. 6.
  3. ↑ 3.0 3.1 Di Battista et al. (1994), p. viii.
  4. ↑ Misue et al. (1995)
  5. ↑ Knuth, Donald E. (2013), "Two thousand years of combinatorics", in Wilson, Robin; Watkins, John J. (eds.), Combinatorics: Ancient and Modern, Oxford University Press, pp. 7–37.
  6. ↑ Holten & van Wijk (2009); Holten et al. (2011).
  7. ↑ Garg & Tamassia (1995).
  8. ↑ Longabaugh (2012).
  9. ↑ Di Battista et al. (1994), Section 2.1.2, Aesthetics, pp. 14–16; Purchase, Cohen & James (1997).
  10. ↑ Di Battista et al. (1994), p 14.
  11. ↑ Di Battista et al. (1994), p. 16.
  12. ↑ 12.0 12.1 Pach & Sharir (2009).
  13. ↑ Published in Grandjean, Martin (2014). "La connaissance est un réseau". Les Cahiers du Numérique. 10 (3): 37–54. doi:10.3166/lcn.10.3.37-54. Retrieved 2014-10-15.
  14. ↑ Di Battista et al. (1994), Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.
  15. ↑ Beckman (1994); Koren (2005).
  16. ↑ Di Battista et al. (1994), Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; 模板:Harv.
  17. ↑ Herman, Melançon & Marshall (2000), Section 2.2, "Traditional Layout – An Overview".
  18. ↑ Sugiyama, Tagawa & Toda (1981); Bastert & Matuszewski (2001); Di Battista et al. (1994), Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.
  19. ↑ Saaty (1964).
  20. ↑ Doğrusöz, Madden & Madden (1997).
  21. ↑ Di Battista et al. (1994), Section 4.7, "Dominance Drawings", pp. 112–127.
  22. ↑ Scott (2000); Brandes, Freeman & Wagner (2014).
  23. ↑ Di Battista et al. (1994), pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; Freese (2004).
  24. ↑ "Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in Jünger & Mutzel (2004).
  25. ↑ GraphPlot Mathematica documentation
  26. ↑ Graph drawing tutorial
  27. ↑ Nachmanson, Robertson & Lee (2008).
  28. ↑ Madden et al. (1996).
  29. ↑ "Tulip – A Huge Graph Visualization Framework", by David Auber, in Jünger & Mutzel (2004).
  30. ↑ "yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in Jünger & Mutzel (2004).
  31. ↑ Tantau (2013); see also the older GD 2012 presentation


General references

General references

一般参考资料

  • Di Battista, Giuseppe

最后1个 Di Battista 最初1个 Giuseppe; [[Peter Eades

作者: 彼得 · 艾德斯|Eades, Peter]]; Tamassia, Roberto; Tollis, Ioannis G.

4 (1994), [http://www.cs.brown.edu/people/rt/gd.html

Http://www.cs.brown.edu/people/rt/gd.html "Algorithms for Drawing Graphs: an Annotated Bibliography 图形绘制的算法: 附有注释的参考书目"], Computational Geometry: Theory and Applications 计算几何: 理论与应用, 4

第四卷 (5

第五期): 235–282

第235-282页, doi:10.1016/0925-7721(94)00014-x {{citation}}: Check |url= value (help); Text "author3-link Roberto Tamassia" ignored (help); Text "first3 Roberto" ignored (help); Text "first4 Ioannis g." ignored (help); Text "last 3 Tamassia" ignored (help); Text "last 4 Tollis" ignored (help); line feed character in |author2-link= at position 12 (help); line feed character in |first1= at position 9 (help); line feed character in |first4= at position 11 (help); line feed character in |issue= at position 2 (help); line feed character in |journal= at position 48 (help); line feed character in |pages= at position 8 (help); line feed character in |title= at position 57 (help); line feed character in |url= at position 42 (help); line feed character in |volume= at position 2 (help). 

| year = 1994 | doi=10.1016/0925-7721(94)00014-x}}.

1994年 | doi 10.1016 / 0925-7721(94)00014-x }。

  • Di Battista, Giuseppe

最后1个 Di Battista 最初1个 Giuseppe; [[Peter Eades

作者: 彼得 · 艾德斯|Eades, Peter]]; Tamassia, Roberto; Tollis, Ioannis G.

4 (1998), Graph Drawing: Algorithms for the Visualization of Graphs 图形绘制: 图形可视化的算法, Prentice Hall

出版商 Prentice Hall, ISBN 978-0-13-301615-4 {{citation}}: Text "author3-link Roberto Tamassia" ignored (help); Text "first3 Roberto" ignored (help); Text "first4 Ioannis g." ignored (help); Text "isbn 978-0-13-301615-4" ignored (help); Text "last 3 Tamassia" ignored (help); Text "last 4 Tollis" ignored (help); line feed character in |author2-link= at position 12 (help); line feed character in |first1= at position 9 (help); line feed character in |first4= at position 11 (help); line feed character in |publisher= at position 14 (help); line feed character in |title= at position 58 (help). 

| year = 1998}}.

1998年。

  • Herman, Ivan

最后1个赫尔曼最初1个伊凡; Melançon, Guy

最后2个梅兰，最初2个盖伊; Marshall, M. Scott

3 m · 斯科特 (2000), "Graph Visualization and Navigation in Information Visualization: A Survey

信息可视化的图形可视化和导航: 一个调查", IEEE Transactions on Visualization and Computer Graphics 可视化与计算机图形学科学杂志, 6

第六卷 (1

第一期): 24–43

第24-43页, doi:[//doi.org/10.1109%2F2945.841119%0A%0A10.1109%20%2F%202945.841119 10.1109/2945.841119 10.1109 / 2945.841119] {{citation}}: Check |doi= value (help); line feed character in |doi= at position 20 (help); line feed character in |first1= at position 5 (help); line feed character in |first2= at position 4 (help); line feed character in |first3= at position 9 (help); line feed character in |issue= at position 2 (help); line feed character in |journal= at position 57 (help); line feed character in |pages= at position 6 (help); line feed character in |title= at position 74 (help); line feed character in |volume= at position 2 (help). 

| year = 2000 }}.

2000年开始。

  • Jünger, Michael

1 j nger; [[Petra Mutzel

2 Petra|Mutzel, Petra]] (2004), Graph Drawing Software 图形绘制软件, Springer-Verlag, ISBN [[Special:BookSources/978-3-540-00881-1

[国际标准图书馆编号978-3-540-00881-1]|978-3-540-00881-1 [国际标准图书馆编号978-3-540-00881-1]]] {{citation}}: Check |isbn= value: invalid character (help); Text "author2-link Petra Mutzel" ignored (help); Text "first1 Michael" ignored (help); Text "出版商 Springer-Verlag" ignored (help); line feed character in |author2-link= at position 13 (help); line feed character in |first1= at position 8 (help); line feed character in |isbn= at position 18 (help); line feed character in |title= at position 23 (help). 

| year = 2004}}.

2004年开始。


Specialized subtopics

Specialized subtopics

专门的副主题

  • Bachmaier, Christian; Brandes, Ulrik; Schreiber, Falk (2014), "Biological Networks", in Tamassia, Roberto (ed.), Handbook of Graph Drawing and Visualization, CRC Press, pp. 621–651.

Http://research.microsoft.com/apps/pubs/default.aspx?id=69611 Theory of Spectral Graph Layout 光谱图布局理论], Tech. Report MSR-TR-94-04

系列技术。Msr-tr-94-04报告, Microsoft Research

微软研究院 {{citation}}: Check |url= value (help); Text "最后一个 Beckman" ignored (help); Text "第一个 Brian" ignored (help); line feed character in |publisher= at position 19 (help); line feed character in |series= at position 26 (help); line feed character in |title= at position 32 (help); line feed character in |url= at position 62 (help). 

| year = 1994}}.

1994年。

  • Brandes, Ulrik; Freeman, Linton C.; Wagner, Dorothea (2014), "Social Networks", in Tamassia, Roberto (ed.), Handbook of Graph Drawing and Visualization, CRC Press, pp. 805–839.
  • Di Battista, Giuseppe; Rimondini, Massimo (2014), "Computer Networks", in Tamassia, Roberto (ed.), Handbook of Graph Drawing and Visualization, CRC Press, pp. 763–803.
  • Doğrusöz, Uğur; Madden, Brendan

2 Madden; Madden, Patrick

最后3个马登最初3个帕特里克 (1997), "Circular layout in the Graph Layout toolkit", in North, Stephen (ed.), [[International Symposium on Graph Drawing

1997年标题链接国际图形绘制专题研讨会|Symposium on Graph Drawing, GD '96 Berkeley, California, USA, September 18–20, 1996, Proceedings 图形绘制研讨会，美国加州伯克利，1996年9月18-20日，美国国家科学院院刊]], Lecture Notes in Computer Science, vol. 1190

第1190卷, Springer-Verlag, pp. 92–100

第92-100页, doi:[//doi.org/10.1007%2F3-540-62495-3_40%0A%0A10.1007%20%2F%203-540-62495-340 10.1007/3-540-62495-3_40 10.1007 / 3-540-62495-340], ISBN 978-3-540-62495-0 {{citation}}: Check |doi= value (help); Invalid |doi-access=free

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}}.

}}.
  • Eiglsperger, Markus

1; Fekete, Sándor; Klau, Gunnar

3 Klau (2001), "Orthogonal graph drawing", in Kaufmann, Michael

1-last Kaufmann; [[Dorothea Wagner

2- 最后一位瓦格纳|Wagner, Dorothea]] (eds.), Drawing Graphs, Lecture Notes in Computer Science, vol. 2025

2025年, Springer Berlin / Heidelberg, pp. 121–171

第121-171页, doi:[//doi.org/10.1007%2F3-540-44969-8_6%0A%0A10.1007%20%2F%203-540-44969-86 10.1007/3-540-44969-8_6 10.1007 / 3-540-44969-86], ISBN [[Special:BookSources/978-3-540-42062-0

2001|978-3-540-42062-0 2001]] {{citation}}: Check |doi= value (help); Check |isbn= value: length (help); Text "2- 第一位多萝西娅" ignored (help); Text "2- 链接多萝西娅 · 瓦格纳" ignored (help); Text "editor1-first Michael" ignored (help); Text "first1 Markus" ignored (help); Text "first3 Gunnar" ignored (help); Text "isbn 978-3-540-42062-0" ignored (help); Text "last 1 Eiglsperger" ignored (help); Text "出版商斯普林格 · 柏林 / 海德堡" ignored (help); Text "计算机科学系列讲稿" ignored (help); Text "贡献正交图绘制" ignored (help); Text "题目绘制图形" ignored (help); line feed character in |doi= at position 24 (help); line feed character in |editor1-first= at position 8 (help); line feed character in |editor2-link= at position 16 (help); line feed character in |first1= at position 7 (help); line feed character in |first3= at position 7 (help); line feed character in |isbn= at position 18 (help); line feed character in |pages= at position 8 (help); line feed character in |volume= at position 5 (help). 

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  • Freese, Ralph

最后一个自由 (2004), "Automated lattice drawing

自动点阵绘图", in Eklund, Peter (ed.), [http://www.math.hawaii.edu/~ralph/Preprints/latdrawing.pdf

Http://www.math.hawaii.edu/~ralph/preprints/latdrawing.pdf Concept Lattices: Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings] (PDF), Lecture Notes in Computer Science, vol. 2961

第2961卷, Springer-Verlag, pp. 589–590

第589-590页, CiteSeerX [//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.6245%0A%0A10.1.1.69.6245 10.1.1.69.6245 10.1.1.69.6245], doi:[//doi.org/10.1007%2F978-3-540-24651-0_12%0A%0A10.1007%20%2F%20978-3-540-24651-012 10.1007/978-3-540-24651-0_12 10.1007 / 978-3-540-24651-012], ISBN [[Special:BookSources/978-3-540-21043-6

2004|978-3-540-21043-6 2004]] {{citation}}: Check |citeseerx= value (help); Check |doi= value (help); Check |isbn= value: length (help); Check |url= value (help); Text "isbn 978-3-540-21043-6" ignored (help); Text "出版商 Springer-Verlag" ignored (help); Text "第一个拉尔夫" ignored (help); Text "编辑-最后埃克伦" ignored (help); Text "编辑-第一彼得" ignored (help); Text "计算机科学系列讲稿" ignored (help); Text "题目概念格: 第二届形式概念分析国际会议，2004年，悉尼，澳大利亚，2004年2月23-26日，会议录" ignored (help); line feed character in |citeseerx= at position 15 (help); line feed character in |contribution= at position 26 (help); line feed character in |doi= at position 29 (help); line feed character in |first= at position 6 (help); line feed character in |isbn= at position 18 (help); line feed character in |pages= at position 8 (help); line feed character in |url= at position 59 (help); line feed character in |volume= at position 5 (help). 

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  • Garg, Ashim

1; Tamassia, Roberto

2 Tamassia (1995), "Upward planarity testing", Order, 12

第12卷 (2

第二期): 109–133

第109-133页, CiteSeerX [//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.2237%0A%0A1995%E5%B9%B410.1.1.10.2237 10.1.1.10.2237 1995年10.1.1.10.2237], doi:10.1007/BF01108622, MR [//www.ams.org/mathscinet-getitem?mr=1354797%0A%0A1354797%E5%85%88%E7%94%9F 1354797 1354797先生] {{citation}}: Check |citeseerx= value (help); Check |mr= value (help); Text "doi 10.1007 / BF01108622" ignored (help); Text "first2 Roberto" ignored (help); Text "日志订单" ignored (help); Text "最后1加格" ignored (help); Text "标题向上平面性测试" ignored (help); Text "首先1阿希姆" ignored (help); line feed character in |citeseerx= at position 15 (help); line feed character in |first1= at position 6 (help); line feed character in |first2= at position 8 (help); line feed character in |issue= at position 2 (help); line feed character in |mr= at position 8 (help); line feed character in |pages= at position 8 (help); line feed character in |volume= at position 3 (help). 

}}.

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  • Holten, Danny; Isenberg, Petra

2 Isenberg; van Wijk, Jarke J.; Fekete, Jean-Daniel

最后4个 Fekete 最早4个 Jean-Daniel (2011), "An extended evaluation of the readability of tapered, animated, and textured directed-edge representations in node-link graphs

对节点链接图中渐变的、动画的和纹理的有向边表示的可读性的扩展评估", [http://www.lri.fr/~isenberg/publications/papers/Holten_2011_AEP.pdf

Http://www.lri.fr/~isenberg/publications/papers/holten_2011_aep.pdf IEEE Pacific Visualization Symposium (PacificVis 2011) 美国电气和电子工程师协会太平洋可视化研讨会(PacificVis 2011)] (PDF), pp. 195–202

第195-202页, doi:[//doi.org/10.1109%2FPACIFICVIS.2011.5742390%0A%0A10.1109%20%2F%20PACIFICVIS.%202011.5742390 10.1109/PACIFICVIS.2011.5742390 10.1109 / PACIFICVIS. 2011.5742390], ISBN 978-1-61284-935-5 {{citation}}: Check |doi= value (help); Check |url= value (help); Text "2011年" ignored (help); Text "author3-link Jack van Wijk" ignored (help); Text "first2 Petra" ignored (help); Text "isbn 978-1-61284-935-5" ignored (help); line feed character in |contribution= at position 127 (help); line feed character in |doi= at position 32 (help); line feed character in |first2= at position 6 (help); line feed character in |first4= at position 12 (help); line feed character in |pages= at position 8 (help); line feed character in |title= at position 55 (help); line feed character in |url= at position 68 (help). 

}}.

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  • Holten

1 Holten, Danny

首先是丹尼; van Wijk 2 van Wijk, Jarke J. (2009

2009年), "A user study on visualizing directed edges in graphs

用户研究图形中的有向边可视化", [https://web.archive.org/web/20111106004500/http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf

Https://web.archive.org/web/20111106004500/http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf Proceedings of the 27th International Conference on Human Factors in Computing Systems (CHI '09)] (PDF), pp. 2299–2308

2299-2308页, CiteSeerX [//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.212.5461%0A%0A10.1.1.212.5461 10.1.1.212.5461 10.1.1.212.5461], doi:[//doi.org/10.1145%2F1518701.1519054%0A%0A10.1145%20%2F%201518701.1519054 10.1145/1518701.1519054 10.1145 / 1518701.1519054], ISBN [[Special:BookSources/9781605582467

9781605582467|9781605582467 9781605582467]], archived from [http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf

Http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf the original] (PDF) on 2011-11-06

2011-11-06 {{citation}}: Check |archiveurl= value (help); Check |citeseerx= value (help); Check |doi= value (help); Check |isbn= value: length (help); Check |url= value (help); Check date values in: |year= and |archivedate= (help); Invalid |url-status=dead

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  • Koren

最后一个韩国, Yehuda

首先是耶胡达 (2005

2005年), "Drawing graphs by eigenvectors: theory and practice 按特征向量绘图: 理论与实践" (PDF), Computers & Mathematics with Applications 计算机与数学与应用》杂志, 49

第49卷 (11–12

第11-12期): 1867–1888

1867-1888页, doi:[//doi.org/10.1016%2Fj.camwa.2004.08.015%0A%0A10.1016%20%2F%20j.camwa.%202004.08 10.1016/j.camwa.2004.08.015 10.1016 / j.camwa. 2004.08], MR [//www.ams.org/mathscinet-getitem?mr=2154691%0A%0A2154691%E5%85%88%E7%94%9F 2154691 2154691先生], archived from [https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/DBLP-journals-camwa-Koren05.pdf

Https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/dblp-journals-camwa-koren05.pdf the original] (PDF) on 2012-04-02

2012-04-02, retrieved 2011-09-17

2011-09-17 {{citation}}: Check |doi= value (help); Check |mr= value (help); Check |url= value (help); Check date values in: |access-date=, |year=, and |archive-date= (help); Invalid |url-status=dead

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}}.

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  • Longabaugh, William

最后一次朗格伯格 (2012

2012年), [http://www.biomedcentral.com/content/pdf/1471-2105-13-275.pdf

Http://www.biomedcentral.com/content/pdf/1471-2105-13-275.pdf "Combing the hairball with BioFabric: a new approach for visualization of large networks 用 BioFabric 梳理毛团: 一种大型网络可视化的新方法"] (PDF), BMC Bioinformatics 生物信息学杂志, 13

第13卷: 275

第275页, doi:[//doi.org/10.1186%2F1471-2105-13-275%0A%0A10.1186%20%2F%201471-2105-13-275 10.1186/1471-2105-13-275 10.1186 / 1471-2105-13-275], PMC 3574047, PMID [//pubmed.ncbi.nlm.nih.gov/23102059

23102059 23102059 23102059] {{citation}}: Check |doi= value (help); Check |pmid= value (help); Check |url= value (help); Check date values in: |year= (help); Text "第一次威廉" ignored (help); line feed character in |doi= at position 25 (help); line feed character in |first= at position 8 (help); line feed character in |journal= at position 19 (help); line feed character in |pages= at position 4 (help); line feed character in |pmid= at position 9 (help); line feed character in |title= at position 88 (help); line feed character in |url= at position 62 (help); line feed character in |volume= at position 3 (help); line feed character in |year= at position 5 (help). 

| pmc=3574047}}.

3574047}.

  • Madden, Brendan

最后一个疯狂橄榄球，最初一个布兰登; Madden, Patrick

2 Madden; Powers, Steve

3 power; Himsolt, Michael

最后4希望 / 最初4迈克尔 (1996), "Portable graph layout and editing

便携式图形布局和编辑", in Brandenburg, Franz J.

最后的勃兰登堡 (ed.), [[International Symposium on Graph Drawing

1996年标题链接国际图形绘制专题研讨会|Graph Drawing: Symposium on Graph Drawing, GD '95, Passau, Germany, September 20–22, 1995, Proceedings 图形绘制: 图形绘制研讨会，GD’95，帕绍，1995年9月20-22日，美国国家科学院院刊]], Lecture Notes in Computer Science, vol. 1027

第1027卷, Springer-Verlag, pp. 385–395

第385-395页, doi:[//doi.org/10.1007%2FBFb0021822%0A%0A10.1007%20%2F%20BFb0021822 10.1007/BFb0021822 10.1007 / BFb0021822], ISBN [[Special:BookSources/978-3-540-60723-6

[国际标准图书编号978-3-540-60723-6]|978-3-540-60723-6 [国际标准图书编号978-3-540-60723-6]]] {{citation}}: Check |doi= value (help); Check |isbn= value: invalid character (help); Invalid |doi-access=free

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}}.

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  • Misue, K.; Eades, P.

2 Eades; Lai, W.

3 Lai; Sugiyama, K.

最后4千。 (1995), "Layout Adjustment and the Mental Map", Journal of Visual Languages and Computing 视觉语言与计算杂志, 6 (2): 183–210, doi:10.1006/jvlc.1995.1010 {{citation}}: Text "first2 p." ignored (help); Text "first3 w." ignored (help); Text "最初1 k。" ignored (help); Text "最后1米苏" ignored (help); Text "标题布局调整和心理地图" ignored (help); line feed character in |first2= at position 3 (help); line feed character in |first3= at position 3 (help); line feed character in |first4= at position 3 (help); line feed character in |journal= at position 42 (help). 

| volume = 6 | number = 2 | pages = 183–210 | year = 1995 | doi=10.1006/jvlc.1995.1010}}.

183-210 | year 1995 | doi 10.1006 / jvlc. 1995.1010}.

  • Nachmanson, Lev

最后1纳克曼森最初1列弗; Robertson, George

2 Robertson; Lee, Bongshin

3 (2008), "Drawing Graphs with GLEE 用 GLEE 绘制图表" (PDF), in Hong, Seok-Hee; Nishizeki, Takao; Quan, Wu (eds.), Graph Drawing, 15th International Symposium, GD 2007, Sydney, Australia, September 24–26, 2007, Revised Papers 15 th International Symposium，GD 2007，Sydney，Australia，September 24-26，Revised Papers, Lecture Notes in Computer Science, vol. 4875

第4875卷, Springer-Verlag, pp. 389–394

第389-394页, doi:[//doi.org/10.1007%2F978-3-540-77537-9_38%0A%0A10.1007%20%2F%20978-3-540-77537-938 10.1007/978-3-540-77537-9_38 10.1007 / 978-3-540-77537-938], ISBN [[Special:BookSources/978-3-540-77536-2

[国际标准图书馆编号978-3-540-77536-2]|978-3-540-77536-2 [国际标准图书馆编号978-3-540-77536-2]]] {{citation}}: Check |doi= value (help); Check |isbn= value: invalid character (help); Invalid |doi-access=free

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}}.

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2|Sharir, Micha]] (2009), "5.5 Angular resolution and slopes", Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures 离散几何及其算法应用: alcal 系列讲座, Mathematical Surveys and Monographs, vol. 152

第152卷, American Mathematical Society

美国数学学会, pp. 126–127

第126-127页 {{citation}}: Text "author2-link Micha Sharir" ignored (help); Text "first2 Micha" ignored (help); Text "last 2 Sharir" ignored (help); Text "系列数学调查和专著" ignored (help); Text "贡献5.5角分辨率及斜坡" ignored (help); line feed character in |author2-link= at position 13 (help); line feed character in |pages= at position 8 (help); line feed character in |publisher= at position 30 (help); line feed character in |title= at position 77 (help); line feed character in |volume= at position 4 (help). 

| year = 2009}}.

2009年开始。

2 Cohen, R. F.; James

最后3名詹姆斯, M. I.

第一季第三集。 (1997

1997年), [https://secure.cs.uvic.ca/twiki/pub/Research/Chisel/ComputationalAestheticsProject/Vol2Nbr4.pdf

Https://secure.cs.uvic.ca/twiki/pub/research/chisel/computationalaestheticsproject/vol2nbr4.pdf "An experimental study of the basis for graph drawing algorithms 关于图形绘制算法基础的实验研究"] (PDF), Journal of Experimental Algorithmics 实验算法杂志, 2

第二卷, Article 4, doi:[//doi.org/10.1145%2F264216.264222%0A%0A10.1145%20%2F%20264216.264222 10.1145/264216.264222 10.1145 / 264216.264222] {{citation}}: Check |doi= value (help); Check |url= value (help); Check date values in: |year= (help); Text "author1-link Helen Purchase" ignored (help); Text "first1 H.c." ignored (help); Text "first2 R.f." ignored (help); Text "最后一次购买" ignored (help); Text "第四条" ignored (help); line feed character in |doi= at position 22 (help); line feed character in |first3= at position 6 (help); line feed character in |journal= at position 37 (help); line feed character in |last2= at position 6 (help); line feed character in |last3= at position 6 (help); line feed character in |title= at position 64 (help); line feed character in |url= at position 96 (help); line feed character in |volume= at position 2 (help); line feed character in |year= at position 5 (help)https://en.wikipedia.org/wiki/Defekte_Weblinks?dwl={{{url}}} Seite nicht mehr abrufbar], Suche in Webarchiven: Kategorie:Wikipedia:Weblink offline (andere Namensräume)[http://timetravel.mementoweb.org/list/2010/Kategorie:Wikipedia:Vorlagenfehler/Vorlage:Toter Link/URL_fehlt . 

}}.

}}.
  • [[Thomas L. Saaty

作者链接: Thomas l. Saaty|Saaty, Thomas L.]] (1964

第三期1964年), "The minimum number of intersections in complete graphs", Proc. Natl. Acad. Sci. U.S.A. 华尔街日报。自然。Acad.科学。美国。, 52

第52卷 (3): 688–690

第688-690页, doi:10.1073/pnas.52.3.688, PMC 300329, PMID 16591215 {{citation}}: Check date values in: |year= (help); Text "标题完全图中的最小交叉点数" ignored (help); line feed character in |authorlink= at position 16 (help); line feed character in |journal= at position 30 (help); line feed character in |pages= at position 8 (help); line feed character in |volume= at position 3 (help); line feed character in |year= at position 5 (help). 

| doi=10.1073/pnas.52.3.688| pmid = 16591215 | pmc = 300329}}.

10.1073 / pnas. 52.3.688 | pmid 16591215 | pmc 300329}.

  • Tantau, Till (2013), "Graph Drawing in TikZ", Journal of Graph Algorithms and Applications 图形算法和应用杂志, 17

第17卷 (4

第四期): 495–513

第495-513页, doi:[//doi.org/10.7155%2Fjgaa.00301%0A%0A10.7155%20%2F%20jgaa.%2000301 10.7155/jgaa.00301 10.7155 / jgaa. 00301] {{citation}}: Check |doi= value (help); Text "title Graph Drawing in TikZ" ignored (help); line feed character in |doi= at position 19 (help); line feed character in |issue= at position 2 (help); line feed character in |journal= at position 45 (help); line feed character in |pages= at position 8 (help); line feed character in |volume= at position 3 (help). 

| year = 2013}}.

2013年开始。


External links

  • GraphX library for .NET: open-source WPF library for graph calculation and visualization. Supports many layout and edge routing algorithms.
  • 模板:Dmoz for many additional links related to graph drawing.


模板:Graph representations


This page was moved from wikipedia:en:Graph drawing. Its edit history can be viewed at 图的绘制/edithistory

取自“https://wiki.swarma.org/index.php?title=图的绘制_Graph_drawing&oldid=7970”