“图的绘制 Graph drawing”的版本间的差异

2020年9月1日 (二) 13:30的版本

本词条由Ryan初步翻译

图1：Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks. 以图的形式展示万维网的一小部分

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交叉领域，它结合了几何图形理论和信息可视化的方法，对来自社会网络分析、制图学、语言学和生物信息学等各种应用场景进行二维描述。

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通过从图形抽象出的顶点和边表示的。这个图不应与图形本身混淆: 非常不同的图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在一起。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 画图公约

图2：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，其中顶点可表示为圆盘、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，他为得到完全图，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，箭头约定俗成的来显示它们的方向; 向上的平面绘图使用以下约定：每个边都从较低的顶点定向到较高的顶点，因此不需要箭头。

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.

节点链接图可被其他画图方式替代，包括邻接表示法，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; 交点表示，其中顶点由非相交的几何对象表示，而边线由其交点表示；可见性表示，其中顶点由平面中的区域表示，边由彼此无障碍视线的区域表示; 汇流图，其中边表示为数学轨迹上的光滑曲线; 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 质量度量

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方法。除了指导针对同一图形的不同布局方法之间的选择之外，某些布局方法还尝试直接优化这些度量。

图3：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]

图的交叉数是相互交叉的边对的数目。如果图形是平面的，那么通常可以方便地画出没有任何边缘相交的图形;也就是说，在本例中，图形绘制表示嵌入图形。然而，应用中经常出现非平面图，因此图形绘制算法通常必须考虑边缘交叉。

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.

一个图形的面积是它的最小边界盒的大小，相对于任意两个顶点之间的最近距离。面积小的画通常比面积大的画更可取，因为它们可以让图画的特征以更大的尺寸显示，因此更清晰。边界框的纵横比也很重要。

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]

对称显示的问题是在给定的图形中找到对称组，并找到尽可能多地显示对称的绘图。一些布局方法自动导致对称图形;另外，一些绘图方法从查找输入图形中的对称性开始，并使用它们来构造绘图。

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.

重要的是，边缘的形状要尽可能简单，以使眼睛更容易跟踪它们。在折线图中，一条边的复杂性可以通过它的弯曲数来衡量，许多方法的目的是提供很少的总弯曲或每条边很少弯曲的图。类似地，对于样条曲线，边的复杂性可以通过边上控制点的数量来度量。

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.

几种常用的质量度量方法与边的长度有关:通常需要最小化边的总长度以及任何边的最大长度。此外，最好使边缘的长度一致而不是变化很大。

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]

角度分辨率是图形绘制中最锐角的度量。如果一个图的顶点高度高，那么它的角分辨率就会很小，但是角分辨率可以由角的函数来限定。

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]

图的斜率数是在具有直线段边(允许交叉)的图中所需的明显边缘斜率的最小值。三次图的斜率数最多为4，五次图的斜率数可能是无界的;4度图的斜率数是否有界仍然是开放的。

Layout methods 布局方法

图4：A force-based network visualization. 基于力的网络可视化 ^[13]

There are many different graph layout strategies:

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]

在基于力的布局系统中，图形绘制软件通过根据基于弹簧系统或分子力学的物理隐喻的力系统不断移动顶点来修改初始顶点的位置。通常，这些系统将相邻顶点之间的吸引力与所有对顶点之间的排斥力结合起来，以寻求一种边长较小而顶点分离良好的布局。这些系统可以执行梯度下降最小化的一个能量函数，或者他们可以把力直接转化为节点的速度或加速度

Spectral layout methods use as coordinates the eigenvectors of a matrix such as the Laplacian derived from the adjacency matrix of the graph.^[15]

频谱布局方法使用从图的邻接矩阵派生的矩阵（例如Laplacian）的特征向量作为坐标。

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]

正交布局方法，允许图形的边缘水平或垂直运行，平行于布局的坐标轴。这些方法最初是为超大规模集成电路和PCB布局问题而设计的，但它们也适用于图形绘制。它们通常涉及到一种多阶段的方法，通过用顶点替换交叉点来平面化输入图，找到一个平面化图的拓扑嵌入，选择边的方向来最小化弯曲，顶点的放置始终与这些方向一致，最后一个布局压缩阶段减少

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]

这些树布局算法显示了一种类似树的根状结构，适合树。通常，在一种称为气球布局的技术中，树中每个节点的子节点被画在围绕该节点的圆上，这些圆的半径在树的较低层次上递减，以便这些圆不会重叠。

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]

分层图绘制方法(通常称为杉山式图)最适合于有向无环图或接近无环的图，例如软件系统中模块或函数之间的依赖关系图。在这些方法中，图的节点使用Coffman Graham算法等方法被安排到水平层中，以这样的方式，大多数边从一层向下到下一层;在这一步之后，将每一层内的节点进行排列，以最小化交叉。

图5：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.

弧图，一种布局风格可以追溯到20世纪60年代，将顶点放在一条直线上;边缘可以画成在直线上方或下方的半圆，也可以画成由多个半圆连接在一起的光滑曲线。

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]

圆形布局方法将图形的顶点放置在一个圆上，仔细选择圆周上顶点的顺序，以减少交叉，并将相邻的顶点放置在彼此接近的位置。边可以画成圆的弦，也可以画成圆内外的弧线。在某些情况下，可以使用多个圆。

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]

当且仅当一个顶点可以从另一个顶点到达时，优势画顶点的方式是:一个顶点向上，或向右，或两个顶点同时向上。这样，布局风格使得图的可达性关系在视觉上变得明显。

Application-specific graph drawings 专用图

Graphs and graph drawings arising in other areas of application include

在其他应用领域出现的图和图绘制包括

Sociograms, drawings of a social network, as often offered by social network analysis software^[22]

社会图，社会网络图，通常由社会网络分析软件提供

Hasse diagrams, a type of graph drawing specialized to partial orders^[23]

哈塞图，一种专门用于部分顺序的图形绘制

Dessin d'enfants, a type of graph drawing used in algebraic geometry 模板:Sfnp

Dessin d'enfants，代数几何中使用的一种图形画法

State diagrams, graphical representations of finite-state machines模板:Sfnp

状态图，有限状态机的图形表示

Computer network diagrams, depictions of the nodes and connections in a computer network 模板:Sfnp

计算机网络图，描述计算机网络中的节点和连接

Flowcharts and drakon-charts, drawings in which the nodes represent the steps of an algorithm and the edges represent control flow between steps.

流程图和drakon图，其中节点表示算法的步骤，边表示步骤之间的控制流的绘图。

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.

数据流程图，其中节点表示信息系统的组件，边缘表示信息从一个组件到另一个组件的移动。

Bioinformatics including phylogenetic trees, protein–protein interaction networks, and metabolic pathways.模板:Sfnp

生物信息学包括系统发育树，蛋白质，蛋白质相互作用网络，和代谢途径。

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（EDA）的布局和布线步骤在很多方面与图形绘制相似，而在分布式计算中贪婪嵌入的问题也是如此，并且图形绘制文献包括从EDA文献中借来的一些结果。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，EDA中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 软件

图6：A graph drawing interface 一个画图软件界面(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:

软件、系统和绘制图形系统的提供者包括:

BioFabric open-source software for visualizing large networks by drawing nodes as horizontal lines.

BioFabric 开源软件，用于通过将节点绘制为水平线来可视化大型网络。

Cytoscape, open-source software for visualizing molecular interaction networks

Cytoscape 可视化分子相互作用网络的开源软件

Gephi, open-source network analysis and visualization software

Gephi 开源网络分析和可视化软件

graph-tool, a free/libre Python library for analysis of graphs.

Graph-Tool 一个免费/免费的Python库，用于分析图形

Graphviz, an open-source graph drawing system from AT&T Corporation^[24]

Graphviz 来自美国电话电报公司的开放源码绘图系统

Linkurious, a commercial network analysis and visualization software for graph databases

Linkurious 图形数据库的商业网络分析和可视化软件

Mathematica, a general purpose computation tool that includes 2D and 3D graph visualization and graph analysis tools.^[25]^[26]

Mathematica 一个通用的计算工具，包括2D和3D图形可视化和图形分析工具。

Microsoft Automatic Graph Layout, open-source .NET library (formerly called GLEE) for laying out graphs^[27]

Microsoft Automatic Graph Layout 用于图表布局的开放源码。net库(以前称为GLEE)

NetworkX is a Python library for studying graphs and networks.

NetworkX 用于研究图和网络的Python库

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.

Tom Sawyer Perspectives是一款基于图形的软件，用于构建企业级图形和数据可视化和分析应用程序。它是一个软件开发工具包(SDK)，具有基于图形的设计和预览环境

Tulip (software),^[29] an open source data visualization tool

Tulip (software)开源数据可视化工具 yEd 具有图形布局功能的图形编辑器

yEd, a graph editor with graph layout functionality^[30]

yEd 具有图形布局功能的图形编辑器

PGF/TikZ 3.0 with the graphdrawing package (requires LuaTeX).^[31]

PGF/TikZ 带graphdrawing软件包的3.0（需要LuaTeX）

LaNet-vi, an open-source large network visualization software

LaNet-vi 开源大型网络可视化软件

Edraw Max 2D business technical diagramming software

Edraw Max 2D商业技术制图软件

References

Footnotes

Footnotes

脚注

↑ 脚本错误：没有“Footnotes”这个模块。, pp. vii–viii; 脚本错误：没有“Footnotes”这个模块。, Section 1.1, "Typical Application Areas".
↑ ^2.0 ^2.1 脚本错误：没有“Footnotes”这个模块。, p. 6.
↑ ^3.0 ^3.1 脚本错误：没有“Footnotes”这个模块。, p. viii.
↑ 脚本错误：没有“Footnotes”这个模块。
↑ 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.
↑ 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。, Section 2.1.2, Aesthetics, pp. 14–16; 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。, p 14.
↑ 脚本错误：没有“Footnotes”这个模块。, p. 16.
↑ ^12.0 ^12.1 脚本错误：没有“Footnotes”这个模块。.
↑ 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.
↑ 脚本错误：没有“Footnotes”这个模块。, Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.
↑ 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。, Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; 模板:Harv.
↑ 脚本错误：没有“Footnotes”这个模块。, Section 2.2, "Traditional Layout – An Overview".
↑ 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。, Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.
↑ 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。, Section 4.7, "Dominance Drawings", pp. 112–127.
↑ 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。, pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; 脚本错误：没有“Footnotes”这个模块。.
↑ "Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in 脚本错误：没有“Footnotes”这个模块。.
↑ GraphPlot Mathematica documentation
↑ Graph drawing tutorial
↑ 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。.
↑ "Tulip – A Huge Graph Visualization Framework", by David Auber, in 脚本错误：没有“Footnotes”这个模块。.
↑ "yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in 脚本错误：没有“Footnotes”这个模块。.
↑ 脚本错误：没有“Footnotes”这个模块。; 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。

Kaufmann, Michael; Wagner, Dorothea, eds. (2001), Drawing Graphs: Methods and Models, Lecture Notes in Computer Science, vol. 2025, Springer-Verlag, doi:10.1007/3-540-44969-8, ISBN 978-3-540-42062-0.

Tamassia, Roberto, ed. (2014), Handbook of Graph Drawing and Visualization, CRC Press, archived from the original on 2013-08-15, retrieved 2013-08-28.

Specialized subtopics

Specialized subtopics

专门的副主题

Anderson, James Andrew; Head, Thomas J. (2006), Automata Theory with Modern Applications, Cambridge University Press, pp. 38–41, ISBN 978-0-521-84887-9.

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

Bastert, Oliver; Matuszewski, Christian (2001), "Layered drawings of digraphs", in Kaufmann, Michael; Wagner, Dorothea (eds.), Drawing Graphs: Methods and Models, Lecture Notes in Computer Science, vol. 2025, Springer-Verlag, pp. 87–120, doi:10.1007/3-540-44969-8_5, ISBN 978-3-540-42062-0.

Beckman, Brian (1994), [http://research.microsoft.com/apps/pubs/default.aspx?id=69611

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

免费访问 (help); Text "first2 Brendan" ignored (help); Text "isbn 978-3-540-62495-0" ignored (help); Text "出版商 Springer-Verlag" ignored (help); Text "编辑-最后的北" ignored (help); Text "编辑-第一斯蒂芬" ignored (help); Text "计算机科学系列讲稿" ignored (help); Text "贡献图形布局工具包中的循环布局" ignored (help); line feed character in |doi-access= at position 5 (help); line feed character in |doi= at position 25 (help); line feed character in |first2= at position 8 (help); line feed character in |first3= at position 8 (help); line feed character in |pages= at position 7 (help); line feed character in |title-link= at position 41 (help); line feed character in |title= at position 97 (help); line feed character in |volume= at position 5 (help).

}}.

}}.

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).

}}.

}}.

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).

}}.

}}.

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).

}}.

}}.

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).

}}.

}}.

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

状态死机 (help); Text "author2-link Jack van Wijk" ignored (help); Text "first2 Jarke j." ignored (help); Text "第27届计算机系统中的人为因素国际会议论文集(CHI’09)" ignored (help); line feed character in |archivedate= at position 11 (help); line feed character in |archiveurl= at position 104 (help); line feed character in |citeseerx= at position 16 (help); line feed character in |contribution= at position 53 (help); line feed character in |doi= at position 24 (help); line feed character in |first1= at position 6 (help); line feed character in |isbn= at position 14 (help); line feed character in |last1= at position 7 (help); line feed character in |last2= at position 9 (help); line feed character in |pages= at position 10 (help); line feed character in |url-status= at position 5 (help); line feed character in |url= at position 61 (help); line feed character in |year= at position 5 (help).

}}.

}}.

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

状态死机 (help); Text "档案-url https://web.archive.org/web/20120402131402/https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/dblp-journals-camwa-koren05.pdf" ignored (help); line feed character in |access-date= at position 11 (help); line feed character in |archive-date= at position 11 (help); line feed character in |doi= at position 28 (help); line feed character in |first= at position 7 (help); line feed character in |issue= at position 6 (help); line feed character in |journal= at position 42 (help); line feed character in |last= at position 6 (help); line feed character in |mr= at position 8 (help); line feed character in |pages= at position 10 (help); line feed character in |title= at position 52 (help); line feed character in |url-status= at position 5 (help); line feed character in |url= at position 104 (help); line feed character in |volume= at position 3 (help); line feed character in |year= at position 5 (help).

}}.

}}.

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

免费访问 (help); Text "first2 Patrick" ignored (help); Text "first3 Steve" ignored (help); Text "出版商 Springer-Verlag" ignored (help); Text "最初的弗朗茨 j。" ignored (help); Text "计算机科学系列讲稿" ignored (help); line feed character in |contribution= at position 34 (help); line feed character in |doi-access= at position 5 (help); line feed character in |doi= at position 19 (help); line feed character in |editor-first= at position 9 (help); line feed character in |first1= at position 8 (help); line feed character in |first2= at position 8 (help); line feed character in |first3= at position 6 (help); line feed character in |first4= at position 8 (help); line feed character in |isbn= at position 18 (help); line feed character in |pages= at position 8 (help); line feed character in |title-link= at position 41 (help); line feed character in |title= at position 103 (help); line feed character in |volume= at position 5 (help).

}}.

}}.

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

免费访问 (help); Text "2008年" ignored (help); Text "contribution-url ftp: / / ftp.research.microsoft. com / pub / tr / tr-2007-72.pdf" ignored (help); Text "first2 George" ignored (help); Text "first3 bongsin" ignored (help); Text "last 3 Lee" ignored (help); Text "出版商 Springer-Verlag" ignored (help); Text "国际图形绘制专题研讨会链接" ignored (help); Text "编辑1-first Seok-Hee" ignored (help); Text "编辑1-last Hong" ignored (help); Text "编辑3-first Wu" ignored (help); Text "编辑3-last Quan" ignored (help); Text "计算机科学系列讲稿" ignored (help); line feed character in |contribution= at position 25 (help); line feed character in |doi-access= at position 5 (help); line feed character in |doi= at position 29 (help); line feed character in |first1= at position 4 (help); line feed character in |first2= at position 7 (help); line feed character in |first3= at position 9 (help); line feed character in |isbn= at position 18 (help); line feed character in |pages= at position 8 (help); line feed character in |title= at position 111 (help); line feed character in |volume= at position 5 (help).

}}.

}}.

Pach, János; [[Micha Sharir

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。

Purchase, H. C.; Cohen

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}.

Scott, John (2000), "Sociograms and Graph Theory", Social network analysis: a handbook (2nd ed.), Sage, pp. 64–69, ISBN 978-0-7619-6339-4.

Sugiyama, Kozo; Tagawa, Shôjirô; Toda, Mitsuhiko (1981), "Methods for visual understanding of hierarchical system structures", IEEE Transactions on Systems, Man, and Cybernetics, SMC-11 (2): 109–125, doi:10.1109/TSMC.1981.4308636, MR 0611436.

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。

Zapponi, Leonardo (August 2003), "What is a Dessin d'Enfant" (PDF), Notices of the American Mathematical Society, 50: 788–789.

External links

GraphX library for .NET: open-source WPF library for graph calculation and visualization. Supports many layout and edge routing algorithms.

Graph drawing e-print archive: including information on papers from all Graph Drawing symposia.

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

[1] 脚本错误：没有“Footnotes”这个模块。, pp. vii–viii; 脚本错误：没有“Footnotes”这个模块。, Section 1.1, "Typical Application Areas".

[dett6-2] 2.0 ^2.1 脚本错误：没有“Footnotes”这个模块。, p. 6.

[dett-viii-3] 3.0 ^3.1 脚本错误：没有“Footnotes”这个模块。, p. viii.

[4] 脚本错误：没有“Footnotes”这个模块。

[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] 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。.

[7] 脚本错误：没有“Footnotes”这个模块。.

[Longabaugh_2012-8] 脚本错误：没有“Footnotes”这个模块。.

[9] 脚本错误：没有“Footnotes”这个模块。, Section 2.1.2, Aesthetics, pp. 14–16; 脚本错误：没有“Footnotes”这个模块。.

[10] 脚本错误：没有“Footnotes”这个模块。, p 14.

[11] 脚本错误：没有“Footnotes”这个模块。, p. 16.

[ps09-12] 12.0 ^12.1 脚本错误：没有“Footnotes”这个模块。.

[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] 脚本错误：没有“Footnotes”这个模块。, Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.

[15] 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。.

[16] 脚本错误：没有“Footnotes”这个模块。, Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; 模板:Harv.

[17] 脚本错误：没有“Footnotes”这个模块。, Section 2.2, "Traditional Layout – An Overview".

[18] 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。, Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.

[19] 脚本错误：没有“Footnotes”这个模块。.

[20] 脚本错误：没有“Footnotes”这个模块。.

[21] 脚本错误：没有“Footnotes”这个模块。, Section 4.7, "Dominance Drawings", pp. 112–127.

[22] 脚本错误：没有“Footnotes”这个模块。; 脚本错误：没有“Footnotes”这个模块。.

[23] 脚本错误：没有“Footnotes”这个模块。, pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; 脚本错误：没有“Footnotes”这个模块。.

[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 脚本错误：没有“Footnotes”这个模块。.

[25] GraphPlot Mathematica documentation

[26] Graph drawing tutorial

[27] 脚本错误：没有“Footnotes”这个模块。.

[28] 脚本错误：没有“Footnotes”这个模块。.

[29] "Tulip – A Huge Graph Visualization Framework", by David Auber, in 脚本错误：没有“Footnotes”这个模块。.

[30] "yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in 脚本错误：没有“Footnotes”这个模块。.

[31] 脚本错误：没有“Footnotes”这个模块。; see also the older GD 2012 presentation

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]