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Moved page from wikipedia:en:Graph drawing (history)
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{{about|the general subject of graph drawing|the annual research symposium|International Symposium on Graph Drawing}}
[[File:WorldWideWebAroundWikipedia.png|thumb|Graphic representation of a minute fraction of the [[WWW]], demonstrating [[hyperlink]]s.]]
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 [[graph (discrete mathematics)|graph]]s arising from applications such as [[social network analysis]], [[cartography]], [[linguistics]], and [[bioinformatics]].<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, pp. vii–viii; {{harvtxt|Herman|Melançon|Marshall|2000}}, Section 1.1, "Typical Application Areas".</ref>
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 [[vertex (graph theory)|vertices]] and [[edge (graph theory)|edges]] of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph.<ref name="dett6">{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. 6.</ref> 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]].<ref name="dett-viii"/> 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.<ref>{{harvtxt|Misue|Eades|Lai|Sugiyama|1995}}</ref>
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==
[[File:4node-digraph-natural.svg|thumb|upright=0.5|[[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 segment]]s, [[Polygonal chain|polylines]], or curves in the [[Euclidean plane]].<ref name="dett-viii">{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. viii.</ref> Node–link diagrams can be traced back to the 13th century work of [[Ramon Llull]], who drew diagrams of this type for [[complete graph]]s in order to analyze all pairwise combinations among sets of metaphysical concepts.<ref>{{citation|contribution=Two thousand years of combinatorics|first=Donald E.|last=Knuth|authorlink=Donald Knuth|pages=7–37|title=Combinatorics: Ancient and Modern|publisher=Oxford University Press|year=2013|editor1-first=Robin|editor1-last=Wilson|editor2-first=John J.|editor2-last=Watkins}}.</ref>
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 graph]]s, [[Arrow (symbol)|arrowheads]] form a commonly used graphical convention to show their [[Orientability|orientation]];<ref name="dett6"/> however, user studies have shown that other conventions such as tapering provide this information more effectively.<ref>{{harvtxt|Holten|van Wijk|2009}}; {{harvtxt|Holten|Isenberg|van Wijk|Fekete|2011}}.</ref> [[Upward planar drawing]] uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.<ref>{{harvtxt|Garg|Tamassia|1995}}.</ref>
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 packing theorem|circle packings]], in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; [[intersection graph|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 track (mathematics)|train tracks]]; fabrics, in which nodes are represented as horizontal lines and edges as vertical lines;<ref name="Longabaugh 2012">{{harvtxt|Longabaugh|2012}}.</ref> 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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 2.1.2, Aesthetics, pp. 14–16; {{harvtxt|Purchase|Cohen|James|1997}}.</ref> 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。
[[File:4node-digraph-embed.svg|upright=0.5|thumb|[[Planar graph]] drawn without overlapping edges]]
[[Planar graph drawn without overlapping edges]]
[[没有重叠边的平面图]]
*The [[Crossing number (graph theory)|crossing number]] of a drawing is the number of pairs of edges that cross each other. If the graph is [[planar graph|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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p 14.</ref>
*The [[Area (graph drawing)|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 [[Graph automorphism|symmetry group]]s 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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. 16.</ref>
*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 [[Bend minimization|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 (graph drawing)|Angular resolution]] is a measure of the sharpest angles in a graph drawing. If a graph has vertices with high [[degree (graph theory)|degree]] then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree.<ref name="ps09">{{harvtxt|Pach|Sharir|2009}}.</ref>
*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 graph]]s 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.<ref name="ps09"/>
==Layout methods==
[[File:Social Network Analysis Visualization.png|thumb|right|A force-based network visualization.<ref>Published in {{Cite journal | volume = 10| issue = 3| last = Grandjean| first = Martin| title = La connaissance est un réseau| journal =Les Cahiers du Numérique| accessdate = 2014-10-15| date = 2014| pages = 37–54| url = http://www.cairn.info/resume.php?ID_ARTICLE=LCN_103_0037| doi=10.3166/lcn.10.3.37-54}}</ref>]]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 [[spring (device)|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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.</ref>
*[[Spectral layout]] methods use as coordinates the [[eigenvector]]s of a [[Matrix (mathematics)|matrix]] such as the [[Discrete Laplace operator|Laplacian]] derived from the [[adjacency matrix]] of the graph.<ref>{{harvtxt|Beckman|1994}}; {{harvtxt|Koren|2005}}.</ref>
*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 [[Printed circuit board|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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; {{harv|Eiglsperger|Fekete|Klau|2001}}.</ref>
*Tree layout algorithms these show a rooted [[tree structure|tree]]-like formation, suitable for [[tree (graph theory)|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.<ref>{{harvtxt|Herman|Melançon|Marshall|2000}}, Section 2.2, "Traditional Layout – An Overview".</ref>
*[[Layered graph drawing]] methods (often called Sugiyama-style drawing) are best suited for [[directed acyclic graph]]s 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.<ref>{{harvtxt|Sugiyama|Tagawa|Toda|1981}}; {{harvtxt|Bastert|Matuszewski|2001}}; {{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.</ref>
[[File:Goldner-Harary-linear.svg|thumb|Arc diagram]]
Arc diagram
弧线图
*[[Arc diagram]]s, a layout style dating back to the 1960s,<ref>{{harvtxt|Saaty|1964}}.</ref> 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.<ref>{{harvtxt|Doğrusöz|Madden|Madden|1997}}.</ref>
*[[Dominance drawing]] places vertices in such a way that one vertex is upwards, rightwards, or both of another if and only if it is [[reachability|reachable]] from the other vertex. In this way, the layout style makes the reachability relation of the graph visually apparent.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 4.7, "Dominance Drawings", pp. 112–127.</ref>
==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
* [[Sociogram]]s, drawings of a [[social network]], as often offered by [[social network analysis software]]<ref>{{Harvard citation text|Scott|2000}}; {{Harvard citation text|Brandes|Freeman|Wagner|2014}}.</ref>
* [[Hasse diagram]]s, a type of graph drawing specialized to [[partial order]]s<ref>{{Harvard citation text|Di Battista|Eades|Tamassia|Tollis|1994}}, pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; {{Harvard citation text|Freese|2004}}.</ref>
* [[Dessin d'enfant]]s, a type of graph drawing used in [[algebraic geometry]]{{sfnp|Zapponi|2003}}
* [[State diagram]]s, graphical representations of [[finite-state machine]]s{{sfnp|Anderson|Head|2006}}
* [[Computer network diagram]]s, depictions of the nodes and connections in a [[computer network]]{{sfnp|Di Battista|Rimondini|2014}}
* [[Flowchart]]s and [[DRAKON|drakon-charts]], drawings in which the nodes represent the steps of an [[algorithm]] and the edges represent [[control flow]] between steps.
* [[Data-flow diagram]]s, 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.
* [[Bioinformatics]] including [[phylogenetic tree]]s, [[protein–protein interaction]] networks, and [[metabolic pathway]]s.{{sfnp|Bachmaier|Brandes|Schreiber|2014}}
In addition, the [[placement (electronic design automation)|placement]] and [[Routing (electronic design automation)|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==
[[File:Gephi 0.9.1 Network Analysis and Visualization Software.png|thumb|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:
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* [[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
* [[graph-tool]], a [[Free Software|free/libre]] [[Python (programming language)|Python]] library for analysis of graphs.
* [[Graphviz]], an open-source graph drawing system from [[AT&T Corporation]]<ref>"Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in {{harvtxt| Jünger|Mutzel|2004}}.</ref>
* [[Linkurious]], a commercial network analysis and visualization software for [[graph databases]]
* [[Mathematica]], a general purpose computation tool that includes 2D and 3D graph visualization and graph analysis tools.<ref>[http://reference.wolfram.com/mathematica/ref/GraphPlot.html GraphPlot] Mathematica documentation</ref><ref>[http://reference.wolfram.com/mathematica/tutorial/GraphDrawingIntroduction.html Graph drawing tutorial]</ref>
* [[Microsoft Automatic Graph Layout]], open-source .NET library (formerly called GLEE) for laying out graphs<ref>{{harvtxt|Nachmanson|Robertson|Lee|2008}}.</ref>
* [[NetworkX]] is a Python library for studying graphs and networks.
* [[Tom Sawyer Software]]<ref>{{harvtxt|Madden|Madden|Powers|Himsolt|1996}}.</ref> 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.
* [[Tulip (software)]],<ref>"Tulip – A Huge Graph Visualization Framework", by David Auber, in {{harvtxt| Jünger|Mutzel|2004}}.</ref> an open source data visualization tool
* [[yEd]], a graph editor with graph layout functionality<ref>"yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in {{harvtxt| Jünger|Mutzel|2004}}.</ref>
* [[PGF/TikZ]] 3.0 with the <code>graphdrawing</code> package (requires [[LuaTeX]]).<ref>{{harvtxt|Tantau|2013}}; see also the older [http://www.tcs.uni-luebeck.de/downloads/mitarbeiter/tantau/2012-gd-presentation.pdf GD 2012 presentation]</ref>
* [[LaNet-vi]], an open-source large network visualization software
* [[Edraw Max]] 2D business technical diagramming software
==References==
;Footnotes
Footnotes
脚注
{{reflist|colwidth=30em}}
;General references
General references
一般参考资料
{{refbegin|colwidth=30em}}
*{{citation
| last1 = Di Battista | first1 = Giuseppe
| last1 = Di Battista | first1 = Giuseppe
最后1个 Di Battista 最初1个 Giuseppe
| last2 = Eades | first2 = Peter | author2-link = Peter Eades
| last2 = Eades | first2 = Peter | author2-link = Peter Eades
作者: 彼得 · 艾德斯
| last3 = Tamassia | first3 = Roberto | author3-link = Roberto Tamassia
| last3 = Tamassia | first3 = Roberto | author3-link = Roberto Tamassia
| last 3 Tamassia | first3 Roberto | author3-link Roberto Tamassia
| last4 = Tollis | first4 = Ioannis G.
| last4 = Tollis | first4 = Ioannis G.
4 | last 4 Tollis | first4 Ioannis g.
| journal = [[Computational Geometry (journal)|Computational Geometry: Theory and Applications]]
| journal = Computational Geometry: Theory and Applications
计算几何: 理论与应用
| pages = 235–282
| pages = 235–282
第235-282页
| title = Algorithms for Drawing Graphs: an Annotated Bibliography
| title = Algorithms for Drawing Graphs: an Annotated Bibliography
图形绘制的算法: 附有注释的参考书目
| url = http://www.cs.brown.edu/people/rt/gd.html
| url = http://www.cs.brown.edu/people/rt/gd.html
Http://www.cs.brown.edu/people/rt/gd.html
| volume = 4
| volume = 4
第四卷
| issue = 5
| issue = 5
第五期
| year = 1994 | doi=10.1016/0925-7721(94)00014-x}}.
| year = 1994 | doi=10.1016/0925-7721(94)00014-x}}.
1994年 | doi 10.1016 / 0925-7721(94)00014-x }。
*{{citation
| last1 = Di Battista | first1 = Giuseppe
| last1 = Di Battista | first1 = Giuseppe
最后1个 Di Battista 最初1个 Giuseppe
| last2 = Eades | first2 = Peter | author2-link = Peter Eades
| last2 = Eades | first2 = Peter | author2-link = Peter Eades
作者: 彼得 · 艾德斯
| last3 = Tamassia | first3 = Roberto | author3-link = Roberto Tamassia
| last3 = Tamassia | first3 = Roberto | author3-link = Roberto Tamassia
| last 3 Tamassia | first3 Roberto | author3-link Roberto Tamassia
| last4 = Tollis | first4 = Ioannis G.
| last4 = Tollis | first4 = Ioannis G.
4 | last 4 Tollis | first4 Ioannis g.
| isbn = 978-0-13-301615-4
| isbn = 978-0-13-301615-4
| isbn 978-0-13-301615-4
| publisher = [[Prentice Hall]]
| publisher = Prentice Hall
出版商 Prentice Hall
| title = Graph Drawing: Algorithms for the Visualization of Graphs
| title = Graph Drawing: Algorithms for the Visualization of Graphs
图形绘制: 图形可视化的算法
| year = 1998}}.
| year = 1998}}.
1998年。
*{{citation
| doi = 10.1109/2945.841119
| doi = 10.1109/2945.841119
10.1109 / 2945.841119
| last1 = Herman | first1 = Ivan
| last1 = Herman | first1 = Ivan
最后1个赫尔曼最初1个伊凡
| last2 = Melançon | first2 = Guy
| last2 = Melançon | first2 = Guy
最后2个梅兰，最初2个盖伊
| last3 = Marshall | first3 = M. Scott
| last3 = Marshall | first3 = M. Scott
3 m · 斯科特
| journal = IEEE Transactions on Visualization and Computer Graphics
| journal = IEEE Transactions on Visualization and Computer Graphics
可视化与计算机图形学科学杂志
| pages = 24–43
| pages = 24–43
第24-43页
| title = Graph Visualization and Navigation in Information Visualization: A Survey
| title = 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
| issue = 1
| issue = 1
第一期
| volume = 6
| volume = 6
第六卷
| year = 2000 }}.
| year = 2000 }}.
2000年开始。
*{{citation
| last1 = Jünger | first1 = Michael
| last1 = Jünger | first1 = Michael
1 j nger | first1 Michael
| last2 = Mutzel | first2 = Petra | author2-link = Petra Mutzel
| last2 = Mutzel | first2 = Petra | author2-link = Petra Mutzel
2 Petra | author2-link Petra Mutzel
| isbn = 978-3-540-00881-1
| isbn = 978-3-540-00881-1
[国际标准图书馆编号978-3-540-00881-1]
| publisher = Springer-Verlag
| publisher = Springer-Verlag
| 出版商 Springer-Verlag
| title = Graph Drawing Software
| title = Graph Drawing Software
图形绘制软件
| year = 2004}}.
| year = 2004}}.
2004年开始。
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{{refend}}
;Specialized subtopics
Specialized subtopics
专门的副主题
{{refbegin|colwidth=30em}}
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| 最后一个 Beckman | 第一个 Brian
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微软研究院
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| series = Tech. Report MSR-TR-94-04
系列技术。Msr-tr-94-04报告
| title = Theory of Spectral Graph Layout
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光谱图布局理论
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Http://research.microsoft.com/apps/pubs/default.aspx?id=69611
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1994年。
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| last1 = Doğrusöz | first1 = Uğur
| last1 = Doğrusöz | first1 = Uğur
| last1 = Doğrusöz | first1 = Uğur
| last2 = Madden | first2 = Brendan
| last2 = Madden | first2 = Brendan
2 Madden | first2 Brendan
| last3 = Madden | first3 = Patrick
| last3 = Madden | first3 = Patrick
最后3个马登最初3个帕特里克
| editor-last = North | editor-first = Stephen
| editor-last = North | editor-first = Stephen
| 编辑-最后的北 | 编辑-第一斯蒂芬
| contribution = Circular layout in the Graph Layout toolkit
| contribution = Circular layout in the Graph Layout toolkit
| 贡献图形布局工具包中的循环布局
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10.1007 / 3-540-62495-340
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第92-100页
| publisher = Springer-Verlag
| publisher = Springer-Verlag
| 出版商 Springer-Verlag
| series = Lecture Notes in Computer Science
| series = Lecture Notes in Computer Science
| 计算机科学系列讲稿
| title = Symposium on Graph Drawing, GD '96 Berkeley, California, USA, September 18–20, 1996, Proceedings
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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
| volume = 1190
| volume = 1190
第1190卷
| year = 1997| title-link = International Symposium on Graph Drawing
| year = 1997| title-link = International Symposium on Graph Drawing
1997年标题链接国际图形绘制专题研讨会
| isbn = 978-3-540-62495-0
| isbn = 978-3-540-62495-0
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免费访问
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| last1 = Eiglsperger | first1 = Markus
| last1 = Eiglsperger | first1 = Markus
1 | last 1 Eiglsperger | first1 Markus
| last2 = Fekete | first2 = Sándor
| last2 = Fekete | first2 = Sándor
| last2 = Fekete | first2 = Sándor
| last3 = Klau | first3 = Gunnar
| last3 = Klau | first3 = Gunnar
3 Klau | first3 Gunnar
| contribution = Orthogonal graph drawing
| contribution = Orthogonal graph drawing
| 贡献正交图绘制
| doi = 10.1007/3-540-44969-8_6
| doi = 10.1007/3-540-44969-8_6
10.1007 / 3-540-44969-86
| editor1-last = Kaufmann | editor1-first = Michael
| editor1-last = Kaufmann | editor1-first = Michael
1-last Kaufmann | editor1-first Michael
| editor2-last = Wagner | editor2-first = Dorothea | editor2-link = Dorothea Wagner
| editor2-last = Wagner | editor2-first = Dorothea | editor2-link = Dorothea Wagner
2- 最后一位瓦格纳 | 2- 第一位多萝西娅 | 2- 链接多萝西娅 · 瓦格纳
| pages = 121–171
| pages = 121–171
第121-171页
| publisher = Springer Berlin / Heidelberg
| publisher = Springer Berlin / Heidelberg
| 出版商斯普林格 · 柏林 / 海德堡
| series = Lecture Notes in Computer Science
| series = Lecture Notes in Computer Science
| 计算机科学系列讲稿
| title = Drawing Graphs
| title = Drawing Graphs
| 题目绘制图形
| volume = 2025
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2025年
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| year = 2001| isbn = 978-3-540-42062-0
2001 | isbn 978-3-540-42062-0
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| last = Freese | first = Ralph
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最后一个自由 | 第一个拉尔夫
| editor-last = Eklund | editor-first = Peter
| editor-last = Eklund | editor-first = Peter
| 编辑-最后埃克伦 | 编辑-第一彼得
| contribution = Automated lattice drawing
| contribution = Automated lattice drawing
自动点阵绘图
| doi = 10.1007/978-3-540-24651-0_12
| doi = 10.1007/978-3-540-24651-0_12
10.1007 / 978-3-540-24651-012
| pages = 589–590
| pages = 589–590
第589-590页
| publisher = Springer-Verlag
| publisher = Springer-Verlag
| 出版商 Springer-Verlag
| series = Lecture Notes in Computer Science
| series = Lecture Notes in Computer Science
| 计算机科学系列讲稿
| title = Concept Lattices: Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings
| title = Concept Lattices: Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings
| 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
| url = http://www.math.hawaii.edu/~ralph/Preprints/latdrawing.pdf
| url = http://www.math.hawaii.edu/~ralph/Preprints/latdrawing.pdf
Http://www.math.hawaii.edu/~ralph/preprints/latdrawing.pdf
| volume = 2961
| volume = 2961
第2961卷
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| year = 2004| isbn = 978-3-540-21043-6
2004 | isbn 978-3-540-21043-6
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1 | 最后1加格 | 首先1阿希姆
| last2 = Tamassia | first2 = Roberto
| last2 = Tamassia | first2 = Roberto
2 Tamassia | first2 Roberto
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| doi 10.1007 / BF01108622
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第二期
| journal = [[Order (journal)|Order]]
| journal = Order
| 日志订单
| mr = 1354797
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1354797先生
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第109-133页
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第12卷
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1995年10.1.1.10.2237
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| last1 = Holten | first1 = Danny
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| last1 = Holten | first1 = Danny
| last2 = Isenberg | first2 = Petra
| last2 = Isenberg | first2 = Petra
2 Isenberg | first2 Petra
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| last3 = van Wijk | first3 = Jarke J.| author3-link Jack van Wijk
| last4 = Fekete | first4 = Jean-Daniel
| last4 = Fekete | first4 = Jean-Daniel
最后4个 Fekete 最早4个 Jean-Daniel
| contribution = An extended evaluation of the readability of tapered, animated, and textured directed-edge representations in node-link graphs
| contribution = 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
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10.1109 / PACIFICVIS. 2011.5742390
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第195-202页
| title = IEEE Pacific Visualization Symposium (PacificVis 2011)
| title = 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)
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|last1 = Holten
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首先是丹尼
|last2 = van Wijk
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2 van Wijk
|first2 = Jarke J.
|first2 = Jarke J.
| first2 Jarke j.
|author2-link = Jack van Wijk
|author2-link = Jack van Wijk
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|contribution = A user study on visualizing directed edges in graphs
|contribution = A user study on visualizing directed edges in graphs
用户研究图形中的有向边可视化
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10.1145 / 1518701.1519054
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2299-2308页
|title = Proceedings of the 27th International Conference on Human Factors in Computing Systems (CHI '09)
|title = Proceedings of the 27th International Conference on Human Factors in Computing Systems (CHI '09)
| 第27届计算机系统中的人为因素国际会议论文集(CHI’09)
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Http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf
|year = 2009
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2009年
|url-status = dead
|url-status = dead
状态死机
|archiveurl = https://web.archive.org/web/20111106004500/http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf
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Https://web.archive.org/web/20111106004500/http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf
|archivedate = 2011-11-06
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2011-11-06
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9781605582467
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| last = Koren
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最后一个韩国
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首先是耶胡达
| doi = 10.1016/j.camwa.2004.08.015
| doi = 10.1016/j.camwa.2004.08.015
10.1016 / j.camwa. 2004.08
| issue = 11–12
| issue = 11–12
第11-12期
| journal = Computers & Mathematics with Applications
| journal = Computers & Mathematics with Applications
计算机与数学与应用》杂志
| mr = 2154691
| mr = 2154691
2154691先生
| pages = 1867–1888
| pages = 1867–1888
1867-1888页
| title = Drawing graphs by eigenvectors: theory and practice
| title = Drawing graphs by eigenvectors: theory and practice
按特征向量绘图: 理论与实践
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Https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/dblp-journals-camwa-koren05.pdf
| volume = 49
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第49卷
| year = 2005
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2005年
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2011-09-17
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| archive-date = 2012-04-02
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2012-04-02
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状态死机
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| last = Longabaugh | first = William
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最后一次朗格伯格 | 第一次威廉
| doi = 10.1186/1471-2105-13-275
| doi = 10.1186/1471-2105-13-275
10.1186 / 1471-2105-13-275
| journal = BMC Bioinformatics
| journal = BMC Bioinformatics
生物信息学杂志
| pages = 275
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第275页
| title = Combing the hairball with BioFabric: a new approach for visualization of large networks
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用 BioFabric 梳理毛团: 一种大型网络可视化的新方法
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Http://www.biomedcentral.com/content/pdf/1471-2105-13-275.pdf
| pmid = 23102059
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23102059
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| year = 2012
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2012年
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| pmc=3574047}}.
3574047}.
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最后一个疯狂橄榄球，最初一个布兰登
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| last2 = Madden | first2 = Patrick
2 Madden | first2 Patrick
| last3 = Powers | first3 = Steve
| last3 = Powers | first3 = Steve
3 power | first3 Steve
| last4 = Himsolt | first4 = Michael
| last4 = Himsolt | first4 = Michael
最后4希望 / 最初4迈克尔
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| editor-last = Brandenburg | editor-first = Franz J.
最后的勃兰登堡 | 最初的弗朗茨 j。
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便携式图形布局和编辑
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10.1007 / BFb0021822
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第385-395页
| publisher = Springer-Verlag
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| 出版商 Springer-Verlag
| series = Lecture Notes in Computer Science
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| 计算机科学系列讲稿
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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
| volume = 1027
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第1027卷
| year = 1996| title-link = International Symposium on Graph Drawing
| year = 1996| title-link = International Symposium on Graph Drawing
1996年标题链接国际图形绘制专题研讨会
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[国际标准图书编号978-3-540-60723-6]
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| last1 = Misue | first1= K.
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| 最后1米苏 | 最初1 k。
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2 Eades | first2 p.
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最后4千。
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视觉语言与计算杂志
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| 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}.
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最后1纳克曼森最初1列弗
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| last2 = Robertson | first2 = George
2 Robertson | first2 George
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| editor1-last = Hong | editor1-first = Seok-Hee
| 编辑1-last Hong | 编辑1-first Seok-Hee
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| editor2-last = Nishizeki | editor2-first = Takao | editor2-link = Takao Nishizeki
| editor2-last = Nishizeki | editor2-first = Takao | editor2-link = Takao Nishizeki
| editor3-last = Quan | editor3-first = Wu
| editor3-last = Quan | editor3-first = Wu
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| contribution = Drawing Graphs with GLEE
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用 GLEE 绘制图表
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10.1007 / 978-3-540-77537-938
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| pages = 389–394
第389-394页
| publisher = Springer-Verlag
| publisher = Springer-Verlag
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| series = Lecture Notes in Computer Science
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| 计算机科学系列讲稿
| title = Graph Drawing, 15th International Symposium, GD 2007, Sydney, Australia, September 24–26, 2007, Revised Papers
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15 th International Symposium，GD 2007，Sydney，Australia，September 24-26，Revised Papers
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第4875卷
| year = 2008| title-link = International Symposium on Graph Drawing
| year = 2008| title-link = International Symposium on Graph Drawing
| 2008年 | 国际图形绘制专题研讨会链接
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[国际标准图书馆编号978-3-540-77536-2]
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免费访问
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| last1 = Pach | first1 = János | author1-link = János Pach
| last1 = Pach | first1 = János | author1-link = János Pach
| last2 = Sharir | first2 = Micha | author2-link = Micha Sharir
| last2 = Sharir | first2 = Micha | author2-link = Micha Sharir
2 | last 2 Sharir | first2 Micha | author2-link Micha Sharir
| contribution = 5.5 Angular resolution and slopes
| contribution = 5.5 Angular resolution and slopes
| 贡献5.5角分辨率及斜坡
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第126-127页
| publisher = [[American Mathematical Society]]
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美国数学学会
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| 系列数学调查和专著
| title = Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures
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离散几何及其算法应用: alcal 系列讲座
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第152卷
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| year = 2009}}.
2009年开始。
*{{citation
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| 最后一次购买
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| first1 H.c.
| author1-link = Helen Purchase
| author1-link = Helen Purchase
| author1-link Helen Purchase
| last2 = Cohen
| last2 = Cohen
2 Cohen
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| first2 R.f.
| last3 = James
| last3 = James
最后3名詹姆斯
| first3 = M. I.
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第一季第三集。
| at = Article 4
| at = Article 4
| 第四条
| doi = 10.1145/264216.264222
| doi = 10.1145/264216.264222
10.1145 / 264216.264222
| journal = Journal of Experimental Algorithmics
| journal = Journal of Experimental Algorithmics
实验算法杂志
| title = An experimental study of the basis for graph drawing algorithms
| title = 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
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Https://secure.cs.uvic.ca/twiki/pub/research/chisel/computationalaestheticsproject/vol2nbr4.pdf
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第二卷
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1997年
}}{{Dead link|date=January 2020 |bot=InternetArchiveBot |fix-attempted=yes }}.
}}.
}}.
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作者链接: Thomas l. Saaty
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| journal = Proc. Natl. Acad. Sci. U.S.A.
华尔街日报。自然。Acad.科学。美国。
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第688-690页
| title = The minimum number of intersections in complete graphs
| title = The minimum number of intersections in complete graphs
| 标题完全图中的最小交叉点数
| volume = 52
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第52卷
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| issue = 3 | year = 1964
第三期1964年
| doi=10.1073/pnas.52.3.688| pmid = 16591215 | pmc = 300329}}.
| doi=10.1073/pnas.52.3.688| pmid = 16591215 | pmc = 300329}}.
10.1073 / pnas. 52.3.688 | pmid 16591215 | pmc 300329}.
*{{citation|title=Social network analysis: a handbook|first=John|last=Scott|edition=2nd|publisher=Sage|year=2000|isbn=978-0-7619-6339-4|contribution=Sociograms and Graph Theory|url=https://books.google.com/books?id=Ww3_bKcz6kgC&pg=PA|pages=64–69}}.
*{{citation|first1=Kozo|last1=Sugiyama|author1-link=Kozo Sugiyama|first2=Shôjirô|last2=Tagawa|first3=Mitsuhiko|last3=Toda|title=Methods for visual understanding of hierarchical system structures|journal=[[IEEE Systems, Man & Cybernetics Society|IEEE Transactions on Systems, Man, and Cybernetics]]|volume=SMC-11|issue=2|pages=109–125|year=1981|mr=0611436|doi=10.1109/TSMC.1981.4308636}}.
*{{citation
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| last = Tantau | first = Till
| last = Tantau | first = Till
| doi = 10.7155/jgaa.00301
| doi = 10.7155/jgaa.00301
10.7155 / jgaa. 00301
| issue = 4
| issue = 4
第四期
| journal = [[Journal of Graph Algorithms and Applications]]
| journal = Journal of Graph Algorithms and Applications
图形算法和应用杂志
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| pages = 495–513
第495-513页
| title = Graph Drawing in TikZ
| title = Graph Drawing in TikZ
| title Graph Drawing in TikZ
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| volume = 17
第17卷
| year = 2013}}.
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2013年开始。
* {{Citation | last1=Zapponi | first1=Leonardo | title=What is a Dessin d'Enfant | url=http://www.ams.org/notices/200307/what-is.pdf | date=August 2003 | journal=[[Notices of the American Mathematical Society]] | volume=50 | pages=788–789}}.
{{refend}}
==External links==
* [http://graphx.codeplex.com GraphX library for .NET]: open-source WPF library for graph calculation and visualization. Supports many layout and edge routing algorithms.
* [http://gdea.informatik.uni-koeln.de/ Graph drawing e-print archive]: including information on papers from all [[International Symposium on Graph Drawing|Graph Drawing symposia]].
* {{dmoz|Science/Math/Combinatorics/Software/Graph_Drawing}} for many additional links related to graph drawing.
{{Graph representations}}
[[Category:Graph drawing| ]]
<noinclude>
<small>This page was moved from [[wikipedia:en:Graph drawing]]. Its edit history can be viewed at [[图的绘制/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{about|the general subject of graph drawing|the annual research symposium|International Symposium on Graph Drawing}}
[[File:WorldWideWebAroundWikipedia.png|thumb|Graphic representation of a minute fraction of the [[WWW]], demonstrating [[hyperlink]]s.]]
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 [[graph (discrete mathematics)|graph]]s arising from applications such as [[social network analysis]], [[cartography]], [[linguistics]], and [[bioinformatics]].<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, pp. vii–viii; {{harvtxt|Herman|Melançon|Marshall|2000}}, Section 1.1, "Typical Application Areas".</ref>
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 [[vertex (graph theory)|vertices]] and [[edge (graph theory)|edges]] of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph.<ref name="dett6">{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. 6.</ref> 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]].<ref name="dett-viii"/> 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.<ref>{{harvtxt|Misue|Eades|Lai|Sugiyama|1995}}</ref>
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==
[[File:4node-digraph-natural.svg|thumb|upright=0.5|[[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 segment]]s, [[Polygonal chain|polylines]], or curves in the [[Euclidean plane]].<ref name="dett-viii">{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. viii.</ref> Node–link diagrams can be traced back to the 13th century work of [[Ramon Llull]], who drew diagrams of this type for [[complete graph]]s in order to analyze all pairwise combinations among sets of metaphysical concepts.<ref>{{citation|contribution=Two thousand years of combinatorics|first=Donald E.|last=Knuth|authorlink=Donald Knuth|pages=7–37|title=Combinatorics: Ancient and Modern|publisher=Oxford University Press|year=2013|editor1-first=Robin|editor1-last=Wilson|editor2-first=John J.|editor2-last=Watkins}}.</ref>
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 graph]]s, [[Arrow (symbol)|arrowheads]] form a commonly used graphical convention to show their [[Orientability|orientation]];<ref name="dett6"/> however, user studies have shown that other conventions such as tapering provide this information more effectively.<ref>{{harvtxt|Holten|van Wijk|2009}}; {{harvtxt|Holten|Isenberg|van Wijk|Fekete|2011}}.</ref> [[Upward planar drawing]] uses the convention that every edge is oriented from a lower vertex to a higher vertex, making arrowheads unnecessary.<ref>{{harvtxt|Garg|Tamassia|1995}}.</ref>
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 packing theorem|circle packings]], in which vertices are represented by disjoint regions in the plane and edges are represented by adjacencies between regions; [[intersection graph|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 track (mathematics)|train tracks]]; fabrics, in which nodes are represented as horizontal lines and edges as vertical lines;<ref name="Longabaugh 2012">{{harvtxt|Longabaugh|2012}}.</ref> 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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 2.1.2, Aesthetics, pp. 14–16; {{harvtxt|Purchase|Cohen|James|1997}}.</ref> 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。
[[File:4node-digraph-embed.svg|upright=0.5|thumb|[[Planar graph]] drawn without overlapping edges]]
[[Planar graph drawn without overlapping edges]]
[[没有重叠边的平面图]]
*The [[Crossing number (graph theory)|crossing number]] of a drawing is the number of pairs of edges that cross each other. If the graph is [[planar graph|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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p 14.</ref>
*The [[Area (graph drawing)|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 [[Graph automorphism|symmetry group]]s 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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. 16.</ref>
*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 [[Bend minimization|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 (graph drawing)|Angular resolution]] is a measure of the sharpest angles in a graph drawing. If a graph has vertices with high [[degree (graph theory)|degree]] then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree.<ref name="ps09">{{harvtxt|Pach|Sharir|2009}}.</ref>
*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 graph]]s 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.<ref name="ps09"/>
==Layout methods==
[[File:Social Network Analysis Visualization.png|thumb|right|A force-based network visualization.<ref>Published in {{Cite journal | volume = 10| issue = 3| last = Grandjean| first = Martin| title = La connaissance est un réseau| journal =Les Cahiers du Numérique| accessdate = 2014-10-15| date = 2014| pages = 37–54| url = http://www.cairn.info/resume.php?ID_ARTICLE=LCN_103_0037| doi=10.3166/lcn.10.3.37-54}}</ref>]]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 [[spring (device)|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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 2.7, "The Force-Directed Approach", pp. 29–30, and Chapter 10, "Force-Directed Methods", pp. 303–326.</ref>
*[[Spectral layout]] methods use as coordinates the [[eigenvector]]s of a [[Matrix (mathematics)|matrix]] such as the [[Discrete Laplace operator|Laplacian]] derived from the [[adjacency matrix]] of the graph.<ref>{{harvtxt|Beckman|1994}}; {{harvtxt|Koren|2005}}.</ref>
*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 [[Printed circuit board|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.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; {{harv|Eiglsperger|Fekete|Klau|2001}}.</ref>
*Tree layout algorithms these show a rooted [[tree structure|tree]]-like formation, suitable for [[tree (graph theory)|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.<ref>{{harvtxt|Herman|Melançon|Marshall|2000}}, Section 2.2, "Traditional Layout – An Overview".</ref>
*[[Layered graph drawing]] methods (often called Sugiyama-style drawing) are best suited for [[directed acyclic graph]]s 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.<ref>{{harvtxt|Sugiyama|Tagawa|Toda|1981}}; {{harvtxt|Bastert|Matuszewski|2001}}; {{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Chapter 9, "Layered Drawings of Digraphs", pp. 265–302.</ref>
[[File:Goldner-Harary-linear.svg|thumb|Arc diagram]]
Arc diagram
弧线图
*[[Arc diagram]]s, a layout style dating back to the 1960s,<ref>{{harvtxt|Saaty|1964}}.</ref> 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.<ref>{{harvtxt|Doğrusöz|Madden|Madden|1997}}.</ref>
*[[Dominance drawing]] places vertices in such a way that one vertex is upwards, rightwards, or both of another if and only if it is [[reachability|reachable]] from the other vertex. In this way, the layout style makes the reachability relation of the graph visually apparent.<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 4.7, "Dominance Drawings", pp. 112–127.</ref>
==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
* [[Sociogram]]s, drawings of a [[social network]], as often offered by [[social network analysis software]]<ref>{{Harvard citation text|Scott|2000}}; {{Harvard citation text|Brandes|Freeman|Wagner|2014}}.</ref>
* [[Hasse diagram]]s, a type of graph drawing specialized to [[partial order]]s<ref>{{Harvard citation text|Di Battista|Eades|Tamassia|Tollis|1994}}, pp. 15–16, and Chapter 6, "Flow and Upward Planarity", pp. 171–214; {{Harvard citation text|Freese|2004}}.</ref>
* [[Dessin d'enfant]]s, a type of graph drawing used in [[algebraic geometry]]{{sfnp|Zapponi|2003}}
* [[State diagram]]s, graphical representations of [[finite-state machine]]s{{sfnp|Anderson|Head|2006}}
* [[Computer network diagram]]s, depictions of the nodes and connections in a [[computer network]]{{sfnp|Di Battista|Rimondini|2014}}
* [[Flowchart]]s and [[DRAKON|drakon-charts]], drawings in which the nodes represent the steps of an [[algorithm]] and the edges represent [[control flow]] between steps.
* [[Data-flow diagram]]s, 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.
* [[Bioinformatics]] including [[phylogenetic tree]]s, [[protein–protein interaction]] networks, and [[metabolic pathway]]s.{{sfnp|Bachmaier|Brandes|Schreiber|2014}}
In addition, the [[placement (electronic design automation)|placement]] and [[Routing (electronic design automation)|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==
[[File:Gephi 0.9.1 Network Analysis and Visualization Software.png|thumb|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:
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* [[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
* [[graph-tool]], a [[Free Software|free/libre]] [[Python (programming language)|Python]] library for analysis of graphs.
* [[Graphviz]], an open-source graph drawing system from [[AT&T Corporation]]<ref>"Graphviz and Dynagraph – Static and Dynamic Graph Drawing Tools", by John Ellson, Emden R. Gansner, Eleftherios Koutsofios, Stephen C. North, and Gordon Woodhull, in {{harvtxt| Jünger|Mutzel|2004}}.</ref>
* [[Linkurious]], a commercial network analysis and visualization software for [[graph databases]]
* [[Mathematica]], a general purpose computation tool that includes 2D and 3D graph visualization and graph analysis tools.<ref>[http://reference.wolfram.com/mathematica/ref/GraphPlot.html GraphPlot] Mathematica documentation</ref><ref>[http://reference.wolfram.com/mathematica/tutorial/GraphDrawingIntroduction.html Graph drawing tutorial]</ref>
* [[Microsoft Automatic Graph Layout]], open-source .NET library (formerly called GLEE) for laying out graphs<ref>{{harvtxt|Nachmanson|Robertson|Lee|2008}}.</ref>
* [[NetworkX]] is a Python library for studying graphs and networks.
* [[Tom Sawyer Software]]<ref>{{harvtxt|Madden|Madden|Powers|Himsolt|1996}}.</ref> 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.
* [[Tulip (software)]],<ref>"Tulip – A Huge Graph Visualization Framework", by David Auber, in {{harvtxt| Jünger|Mutzel|2004}}.</ref> an open source data visualization tool
* [[yEd]], a graph editor with graph layout functionality<ref>"yFiles – Visualization and Automatic Layout of Graphs", by Roland Wiese, Markus Eiglsperger, and Michael Kaufmann, in {{harvtxt| Jünger|Mutzel|2004}}.</ref>
* [[PGF/TikZ]] 3.0 with the <code>graphdrawing</code> package (requires [[LuaTeX]]).<ref>{{harvtxt|Tantau|2013}}; see also the older [http://www.tcs.uni-luebeck.de/downloads/mitarbeiter/tantau/2012-gd-presentation.pdf GD 2012 presentation]</ref>
* [[LaNet-vi]], an open-source large network visualization software
* [[Edraw Max]] 2D business technical diagramming software
==References==
;Footnotes
Footnotes
脚注
{{reflist|colwidth=30em}}
;General references
General references
一般参考资料
{{refbegin|colwidth=30em}}
*{{citation
| last1 = Di Battista | first1 = Giuseppe
| last1 = Di Battista | first1 = Giuseppe
最后1个 Di Battista 最初1个 Giuseppe
| last2 = Eades | first2 = Peter | author2-link = Peter Eades
| last2 = Eades | first2 = Peter | author2-link = Peter Eades
作者: 彼得 · 艾德斯
| last3 = Tamassia | first3 = Roberto | author3-link = Roberto Tamassia
| last3 = Tamassia | first3 = Roberto | author3-link = Roberto Tamassia
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最后1个 Di Battista 最初1个 Giuseppe
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作者: 彼得 · 艾德斯
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出版商 Prentice Hall
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最后1个赫尔曼最初1个伊凡
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最后2个梅兰，最初2个盖伊
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3 m · 斯科特
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可视化与计算机图形学科学杂志
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[国际标准图书馆编号978-3-540-00881-1]
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{{refend}}
;Specialized subtopics
Specialized subtopics
专门的副主题
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系列技术。Msr-tr-94-04报告
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光谱图布局理论
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2 Madden | first2 Brendan
| last3 = Madden | first3 = Patrick
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最后3个马登最初3个帕特里克
| editor-last = North | editor-first = Stephen
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| 编辑-最后的北 | 编辑-第一斯蒂芬
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1997年标题链接国际图形绘制专题研讨会
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3 Klau | first3 Gunnar
| contribution = Orthogonal graph drawing
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2- 最后一位瓦格纳 | 2- 第一位多萝西娅 | 2- 链接多萝西娅 · 瓦格纳
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第121-171页
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最后一个自由 | 第一个拉尔夫
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| 编辑-最后埃克伦 | 编辑-第一彼得
| contribution = Automated lattice drawing
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自动点阵绘图
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第589-590页
| publisher = Springer-Verlag
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| 计算机科学系列讲稿
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1354797先生
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第109-133页
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最后4个 Fekete 最早4个 Jean-Daniel
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首先是丹尼
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用户研究图形中的有向边可视化
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2009年
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状态死机
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最后一个韩国
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首先是耶胡达
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第11-12期
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计算机与数学与应用》杂志
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2154691先生
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1867-1888页
| title = Drawing graphs by eigenvectors: theory and practice
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按特征向量绘图: 理论与实践
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Https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/dblp-journals-camwa-koren05.pdf
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状态死机
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最后一次朗格伯格 | 第一次威廉
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10.1186 / 1471-2105-13-275
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生物信息学杂志
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用 BioFabric 梳理毛团: 一种大型网络可视化的新方法
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最后一个疯狂橄榄球，最初一个布兰登
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2 Madden | first2 Patrick
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3 power | first3 Steve
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最后4希望 / 最初4迈克尔
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最后的勃兰登堡 | 最初的弗朗茨 j。
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便携式图形布局和编辑
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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
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1996年标题链接国际图形绘制专题研讨会
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3 Lai | first3 w.
| last4 = Sugiyama | first4 = K.
| last4 = Sugiyama | first4 = K.
最后4千。
| title = Layout Adjustment and the Mental Map
| title = Layout Adjustment and the Mental Map
| 标题布局调整和心理地图
| journal = Journal of Visual Languages and Computing
| journal = Journal of Visual Languages and Computing
视觉语言与计算杂志
| volume = 6 | number = 2 | pages = 183–210 | year = 1995 | doi=10.1006/jvlc.1995.1010}}.
| 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}.
*{{citation
| last1 = Nachmanson | first1 = Lev
| last1 = Nachmanson | first1 = Lev
最后1纳克曼森最初1列弗
| last2 = Robertson | first2 = George
| last2 = Robertson | first2 = George
2 Robertson | first2 George
| last3 = Lee | first3 = Bongshin
| last3 = Lee | first3 = Bongshin
3 | last 3 Lee | first3 bongsin
| editor1-last = Hong | editor1-first = Seok-Hee
| editor1-last = Hong | editor1-first = Seok-Hee
| 编辑1-last Hong | 编辑1-first Seok-Hee
| editor2-last = Nishizeki | editor2-first = Takao | editor2-link = Takao Nishizeki
| editor2-last = Nishizeki | editor2-first = Takao | editor2-link = Takao Nishizeki
| editor2-last = Nishizeki | editor2-first = Takao | editor2-link = Takao Nishizeki
| editor3-last = Quan | editor3-first = Wu
| editor3-last = Quan | editor3-first = Wu
| 编辑3-last Quan | 编辑3-first Wu
| contribution = Drawing Graphs with GLEE
| contribution = Drawing Graphs with GLEE
用 GLEE 绘制图表
| doi = 10.1007/978-3-540-77537-9_38
| doi = 10.1007/978-3-540-77537-9_38
10.1007 / 978-3-540-77537-938
| pages = 389–394
| pages = 389–394
第389-394页
| publisher = Springer-Verlag
| publisher = Springer-Verlag
| 出版商 Springer-Verlag
| series = Lecture Notes in Computer Science
| series = Lecture Notes in Computer Science
| 计算机科学系列讲稿
| title = Graph Drawing, 15th International Symposium, GD 2007, Sydney, Australia, September 24–26, 2007, Revised Papers
| title = 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
| contribution-url = ftp://ftp.research.microsoft.com/pub/TR/TR-2007-72.pdf
| contribution-url = ftp://ftp.research.microsoft.com/pub/TR/TR-2007-72.pdf
| contribution-url ftp: / / ftp.research.microsoft. com / pub / tr / tr-2007-72.pdf
| volume = 4875
| volume = 4875
第4875卷
| year = 2008| title-link = International Symposium on Graph Drawing
| year = 2008| title-link = International Symposium on Graph Drawing
| 2008年 | 国际图形绘制专题研讨会链接
| isbn = 978-3-540-77536-2
| isbn = 978-3-540-77536-2
[国际标准图书馆编号978-3-540-77536-2]
| doi-access = free
| doi-access = free
免费访问
}}.
}}.
}}.
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| last1 = Pach | first1 = János | author1-link = János Pach
| last1 = Pach | first1 = János | author1-link = János Pach
| last1 = Pach | first1 = János | author1-link = János Pach
| last2 = Sharir | first2 = Micha | author2-link = Micha Sharir
| last2 = Sharir | first2 = Micha | author2-link = Micha Sharir
2 | last 2 Sharir | first2 Micha | author2-link Micha Sharir
| contribution = 5.5 Angular resolution and slopes
| contribution = 5.5 Angular resolution and slopes
| 贡献5.5角分辨率及斜坡
| pages = 126–127
| pages = 126–127
第126-127页
| publisher = [[American Mathematical Society]]
| publisher = American Mathematical Society
美国数学学会
| series = Mathematical Surveys and Monographs
| series = Mathematical Surveys and Monographs
| 系列数学调查和专著
| title = Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures
| title = Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures
离散几何及其算法应用: alcal 系列讲座
| volume = 152
| volume = 152
第152卷
| year = 2009}}.
| year = 2009}}.
2009年开始。
*{{citation
| last1 = Purchase
| last1 = Purchase
| 最后一次购买
| first1 = H. C.
| first1 = H. C.
| first1 H.c.
| author1-link = Helen Purchase
| author1-link = Helen Purchase
| author1-link Helen Purchase
| last2 = Cohen
| last2 = Cohen
2 Cohen
| first2 = R. F.
| first2 = R. F.
| first2 R.f.
| last3 = James
| last3 = James
最后3名詹姆斯
| first3 = M. I.
| first3 = M. I.
第一季第三集。
| at = Article 4
| at = Article 4
| 第四条
| doi = 10.1145/264216.264222
| doi = 10.1145/264216.264222
10.1145 / 264216.264222
| journal = Journal of Experimental Algorithmics
| journal = Journal of Experimental Algorithmics
实验算法杂志
| title = An experimental study of the basis for graph drawing algorithms
| title = 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
| url = https://secure.cs.uvic.ca/twiki/pub/Research/Chisel/ComputationalAestheticsProject/Vol2Nbr4.pdf
| url = https://secure.cs.uvic.ca/twiki/pub/Research/Chisel/ComputationalAestheticsProject/Vol2Nbr4.pdf
Https://secure.cs.uvic.ca/twiki/pub/research/chisel/computationalaestheticsproject/vol2nbr4.pdf
| volume = 2
| volume = 2
第二卷
| year = 1997
| year = 1997
1997年
}}{{Dead link|date=January 2020 |bot=InternetArchiveBot |fix-attempted=yes }}.
}}.
}}.
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| last = Saaty | first = Thomas L. | authorlink = Thomas L. Saaty
| last = Saaty | first = Thomas L. | authorlink = Thomas L. Saaty
作者链接: Thomas l. Saaty
| journal = Proc. Natl. Acad. Sci. U.S.A.
| journal = Proc. Natl. Acad. Sci. U.S.A.
华尔街日报。自然。Acad.科学。美国。
| pages = 688–690
| pages = 688–690
第688-690页
| title = The minimum number of intersections in complete graphs
| title = The minimum number of intersections in complete graphs
| 标题完全图中的最小交叉点数
| volume = 52
| volume = 52
第52卷
| issue = 3 | year = 1964
| issue = 3 | year = 1964
第三期1964年
| doi=10.1073/pnas.52.3.688| pmid = 16591215 | pmc = 300329}}.
| doi=10.1073/pnas.52.3.688| pmid = 16591215 | pmc = 300329}}.
10.1073 / pnas. 52.3.688 | pmid 16591215 | pmc 300329}.
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*{{citation|first1=Kozo|last1=Sugiyama|author1-link=Kozo Sugiyama|first2=Shôjirô|last2=Tagawa|first3=Mitsuhiko|last3=Toda|title=Methods for visual understanding of hierarchical system structures|journal=[[IEEE Systems, Man & Cybernetics Society|IEEE Transactions on Systems, Man, and Cybernetics]]|volume=SMC-11|issue=2|pages=109–125|year=1981|mr=0611436|doi=10.1109/TSMC.1981.4308636}}.
*{{citation
| last = Tantau | first = Till
| last = Tantau | first = Till
| last = Tantau | first = Till
| doi = 10.7155/jgaa.00301
| doi = 10.7155/jgaa.00301
10.7155 / jgaa. 00301
| issue = 4
| issue = 4
第四期
| journal = [[Journal of Graph Algorithms and Applications]]
| journal = Journal of Graph Algorithms and Applications
图形算法和应用杂志
| pages = 495–513
| pages = 495–513
第495-513页
| title = Graph Drawing in TikZ
| title = Graph Drawing in TikZ
| title Graph Drawing in TikZ
| volume = 17
| volume = 17
第17卷
| year = 2013}}.
| year = 2013}}.
2013年开始。
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{{refend}}
==External links==
* [http://graphx.codeplex.com GraphX library for .NET]: open-source WPF library for graph calculation and visualization. Supports many layout and edge routing algorithms.
* [http://gdea.informatik.uni-koeln.de/ Graph drawing e-print archive]: including information on papers from all [[International Symposium on Graph Drawing|Graph Drawing symposia]].
* {{dmoz|Science/Math/Combinatorics/Software/Graph_Drawing}} for many additional links related to graph drawing.
{{Graph representations}}
[[Category:Graph drawing| ]]
<noinclude>
<small>This page was moved from [[wikipedia:en:Graph drawing]]. Its edit history can be viewed at [[图的绘制/edithistory]]</small></noinclude>
[[Category:待整理页面]]