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第1行： − 于2020.11.19再次审校，若有遗漏敬请谅解。 − {{about|the general subject of graph drawing|the annual research symposium|International Symposium on Graph Drawing}}+ − + − − 图1：Graphic representation of a minute fraction of the [[WWW]], demonstrating [[hyperlink]]s. 以图的形式展示万维网的一小部分]] − − − − − − − '''图的绘制 Graph Drawing'''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 geometric graph theory</font>]]'''和 '''[[信息可视化 information visualization]]'''的方法，可以用于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。 第30行：
第20行： − 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，例如圆堆积，其中，顶点由平面中的不相交区域表示，边缘由区域之间的邻接表示； 交点表示，其中顶点由不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，边缘由彼此无障碍视线的区域表示； 融合图，其中边缘表示为数学火车轨道内的平滑曲线； 织物，其中节点表示为水平线，边缘表示为垂直线； 以及图表的邻接矩阵的可视化。 − − 节点链接图的替代绘制替代，包括邻接表示法，如'''圆填充 Circle Packings'''，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； '''<font color="#ff8000">交点表示 Intersection representations</font>'''，其中顶点由非相交的几何对象表示，而边由其交点表示；可见性：其中顶点由平面中的区域表示，边由彼此无视线障碍的区域表示; 汇流图，其中边表示为数学轨迹上的光滑曲线; 连接物，其中顶点表示为水平线，边表示为垂直线; 以及图形'''<font color="#ff8000">邻接矩阵 Adjiacency Matrix</font>'''的可视化结点。 − 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，我们定义了许多不同的图形质量度量方法。除了用于指导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度量方式。 − − [[File:4node-digraph-embed.svg|upright=0.5|thumb| − 图3：[[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> − 图的'''<font color="#ff8000">交叉数 Crossing Number</font>'''是相交的成对的边的数目。如果图形是平面的，那么我们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'''<font color="#ff8000">图形嵌入 Graph Embedding</font>'''。然而，实际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 (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. − 一个图形的面积是它的最小'''<font color="#ff8000">边界盒 Bounding Box</font>'''的大小，与任意两个顶点之间的最近距离有关。面积小的图通常比面积大的图更可取，因为它们可以让图画的特征以更大的尺寸显示，从而更醒目。当然，边框的纵横比也很重要。 − − *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> − 对称显示的问题是在给定的图形中找到'''<font color="#ff8000">对称组 Symmetry Groups</font>'''，并找到尽可能多地显示对称的绘图。一些布局方法自动形成对称图形;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 [[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.+ − 重要的是，边缘的形状要尽可能简单，以便更容易循着它们的轨迹观察。在折线图中，一条边的复杂性可以通过它的弯曲数来衡量，多数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差别很大。 − + − − + − 图的'''<font color="#ff8000">斜率 Slope Number</font>'''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。'''<font color="#ff8000">三次图 Cubic Graphs</font>'''的斜率最大为4，五次图的斜率数可能是无界的，但四次的图的斜率是否有界仍然有待求证的。 − + − [[File:Social Network Analysis Visualization.png|thumb|right|+ − 图4：A force-based network visualization. 基于力的网络可视化 <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:+ − There are many different graph layout strategies:+ − 有许多不同的图形布局方法:+ − *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> − 在'''<font color="#ff8000">'基于力的布局系统 Force-Based Layout</font>''中，图形绘制软件根据基于弹簧系统或分子力学的物理隐含的力系统，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'''<font color="#ff8000">梯度下降 Gradient Descent</font>'''最小化的能量函数，或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 [[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> − '''<font color="#ff8000">频谱布局方法 Spectral Layout</font>'''，以从图的邻接矩阵派生的矩阵（例如Laplacian）的'''<font color="#ff8000">特征向量 Eigenvector</font>'''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 [[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>+ − 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图形面积。 − *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>+ − 这些树形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，树形图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，因此这些圆不会重叠。 − *[[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>+ − '''<font color="#ff8000">分层图绘制方法 Layered Graph Drawing</font>'''(通常称为杉山式图)最适合于'''<font color="#ff8000">有向无环图 Directed Acyclic Graphs</font>'''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。 − [[File:Goldner-Harary-linear.svg|thumb|+ − 图5：Arc diagram 弧线图]] + − + − '''<font color="#ff8000">弧图 Arc Diagram</font>'''，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。 − + − '''<font color="#ff8000">圆形布局方法 Circular Layout</font>'''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。 − + − '''<font color="#ff8000">优势图 Dominance Drawing</font>'''当且仅当一个顶点可以从另一个顶点到达时，画顶点的最优方式是: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+ − 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+ − * [[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>+ − '''<font color="#ff8000">社会图 Sociogram</font>'''，社会网络图，通常由社会网络分析软件提供 − + − '''<font color="#ff8000">哈塞图 Hasse Diagram</font>'''，一种专门用于部分顺序的图形绘制 − + − − + − − + − '''<font color="#ff8000">计算机网络图 Computer Network Diagram</font>'''，描述计算机网络中的节点和连接 − + − − + − − + − 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 (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，'''<font color="#ff8000">电子设计自动化（EDA）Electronic Design Automation</font>'''的布局和布线步骤在很多方面与图形绘制相似，而在'''<font color="#ff8000">分布式计算 Distributed Computing</font>'''中'''<font color="#ff8000">贪婪嵌入 Greedy Embedding</font>'''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。 − + − + − − − A graph drawing interface ([[Gephi 0.9.1)]]Software, systems, and providers of systems for drawing graphs include: 第165行：
第111行： − + − BioFabric 开源软件，用于将节点绘制为水平线来可视化大型网络。 − + − Cytoscape 可视化分子相互作用网络的开源软件 − + − Gephi 开源网络分析和可视化软件 − + − − + − Graphviz 来自美国电话电报公司的开放源码绘图系统 − + − Linkurious 图形数据库的商业网络分析和可视化软件 − + − 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 用于图表布局的开放源码。net库(以前称为GLEE) − + − NetworkX 用于研究图和网络的Python库 − + − 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)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 具有图形布局功能的图形编辑器 − + − PGF/TikZ 带graphdrawing软件包的3.0（需要LuaTeX） − + − LaNet-vi 开源大型网络可视化软件 − + − Edraw Max 2D商业技术制图软件 − − ;Footnotes − − Footnotes − − 脚注 − + 第235行：
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无编辑摘要
本词条由Ryan初步翻译
本词条由Ryan初步翻译
由CecileLi初步审校
由CecileLi初步审校
[[File:WorldWideWebAroundWikipedia.png|thumb|图1：以图的形式展示万维网的一小部分]]
'''图的绘制 Graph drawing'''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 geometric graph theory</font>]]'''和 '''[[信息可视化 information visualization]]'''的方法，可以用于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。<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, pp. vii–viii; {{harvtxt|Herman|Melançon|Marshall|2000}}, Section 1.1, "Typical Application Areas".</ref>
[[File:WorldWideWebAroundWikipedia.png|thumb|
'''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>
节点链接图的替代约定包括：
:*邻接表示，例如圆堆积 circle packings，其中，顶点由平面中的不相交区域表示，边缘由区域之间的邻接表示；
:*交点表示，其中顶点由不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，边缘由彼此无障碍视线的区域表示；
:*融合图，其中边缘表示为数学火车轨道内的平滑曲线；
:*织物，其中节点表示为水平线，边缘表示为垂直线；<ref name="Longabaugh 2012">{{harvtxt|Longabaugh|2012}}.</ref>
:*图表的[[邻接矩阵]]的可视化。
== 质量度量 Quality measures==
== 质量度量 Quality measures==
为了找到客观评价图形美观性和可用性的方法，我们定义了许多不同的图形质量度量方法。<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 2.1.2, Aesthetics, pp. 14–16; {{harvtxt|Purchase|Cohen|James|1997}}.</ref>除了用于指导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度量方式。
[[File:4node-digraph-embed.svg|upright=0.5|thumb|图3：没有重叠边的平面图]]
*[[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>
*图的'''交叉数 Crossing number'''是相交的成对的边的数目。如果图形是平面的，那么我们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'''<font color="#ff8000">图形嵌入 Graph embedding</font>'''。然而，实际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。<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p 14.</ref>
'''<font color="#ff8000">角度分辨率 Angular Resolution</font>'''是图形绘制中最小的锐角的度数。如果一个图的顶点高度高，那么它的角分辨率就很小，但是角分辨率也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 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"/>
*一个图形的面积是它的最小'''<font color="#ff8000">边界盒 bounding box</font>'''的大小，与任意两个顶点之间的最近距离有关。面积小的图通常比面积大的图更可取，因为它们可以让图画的特征以更大的尺寸显示，从而更醒目。当然，边框的纵横比也很重要。
==Layout methods 布局方法==
*对称显示的问题是在给定的图形中找到'''<font color="#ff8000">对称组 Symmetry Groups</font>'''，并找到尽可能多地显示对称的绘图。一些布局方法自动形成对称图形;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。<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, p. 16.</ref>
*重要的是，边缘的形状要尽可能简单，以便更容易循着它们的轨迹观察。在折线图中，一条边的复杂性可以通过它的弯曲数来衡量，多数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。
*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差别很大。
*'''<font color="#ff8000">角度分辨率 Angular resolution</font>'''是图形绘制中最小的锐角的度数。如果一个图的顶点高度高，那么它的角分辨率就很小，但是角分辨率也可以由角的函数来限定。<ref name="ps09">{{harvtxt|Pach|Sharir|2009}}.</ref>
*图的'''<font color="#ff8000">斜率 slope number</font>'''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。'''<font color="#ff8000">三次图 Cubic Graphs</font>'''的斜率最大为4，五次图的斜率数可能是无界的，但四次的图的斜率是否有界仍然有待求证的。<ref name="ps09"/>
==布局方法 Layout methods ==
[[File:Social Network Analysis Visualization.png|thumb|right|图4：基于力的网络可视化 <ref>{{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>]]
有许多不同的图形布局方法，如下
*在'''<font color="#ff8000">'基于力的布局系统 Force-Based Layout</font>''中，图形绘制软件根据基于弹簧系统或分子力学的物理隐含的力系统，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'''<font color="#ff8000">梯度下降 gradient descent</font>'''最小化的能量函数，或可以把力直接转化为节点的速度或加速度。<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>
*'''<font color="#ff8000">频谱布局法 Spectral layout</font>'''，以从图的[[邻接矩阵]]派生的矩阵（例如Laplacian）的'''<font color="#ff8000">特征向量 Eigenvector</font>'''作为坐标。<ref>{{harvtxt|Beckman|1994}}; {{harvtxt|Koren|2005}}.</ref>
*[[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.
*'''正交布局法 Orthogonal layout methods'''，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图形面积。<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Chapter 5, "Flow and Orthogonal Drawings", pp. 137–170; {{harv|Eiglsperger|Fekete|Klau|2001}}.</ref>
*[[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>
*'''树形布局'''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，树形图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，因此这些圆不会重叠。<ref>{{harvtxt|Herman|Melançon|Marshall|2000}}, Section 2.2, "Traditional Layout – An Overview".</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>
*'''<font color="#ff8000">分层图绘制方法 Layered graph drawing</font>'''(通常称为'''杉山式图 Sugiyama-style drawing''')最适合于'''<font color="#ff8000">有向无环图 directed acyclic graphs</font>'''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，使交叉最少。<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|图5：弧线图]]
*'''<font color="#ff8000">弧线图 Arc Diagram</font>'''，这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。
*'''<font color="#ff8000">圆形布局法 Circular Layout</font>'''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。<ref>{{harvtxt|Doğrusöz|Madden|Madden|1997}}.</ref>
*'''<font color="#ff8000">优势图 Dominance drawing</font>'''当且仅当一个顶点可以从另一个顶点到达时，画顶点的最优方式是：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。<ref>{{harvtxt|Di Battista|Eades|Tamassia|Tollis|1994}}, Section 4.7, "Dominance Drawings", pp. 112–127.</ref>
==专用图==
在其他应用领域出现的图和图绘制包括：
* [[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>
* '''社会图 Sociogram'''，社会网络图，通常由社会网络分析软件提供；<ref>{{Harvard citation text|Scott|2000}}; {{Harvard citation text|Brandes|Freeman|Wagner|2014}}.</ref>
* [[Dessin d'enfant]]s, a type of graph drawing used in [[algebraic geometry]]{{sfnp|Zapponi|2003}}
* '''<font color="#ff8000">哈塞图 Hasse diagram</font>'''，一种专门用于部分顺序的图形绘制<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>
'''<font color="#ff8000">'Dessin d'enfants</font>''，代数几何中使用的一种图形画法
* [[State diagram]]s, graphical representations of [[finite-state machine]]s{{sfnp|Anderson|Head|2006}}
* '''<font color="#ff8000">Dessin d'enfants</font>''，代数几何中使用的一种图形画法；{{sfnp|Zapponi|2003}}
'''<font color="#ff8000">状态图 State Diagram</font>'''，有限状态机的图形表示
* [[Computer network diagram]]s, depictions of the nodes and connections in a [[computer network]]{{sfnp|Di Battista|Rimondini|2014}}
*'''状态图 State diagram'''，有限状态机的图形表示；{{sfnp|Anderson|Head|2006}}
* [[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.
*'''计算机网络图 Computer network diagram'''，描述计算机网络中的节点和连接；{{sfnp|Di Battista|Rimondini|2014}}
'''<font color="#ff8000">流程图 Flowchart</font>'''和'''<font color="#ff8000">drakon图</font>'''，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 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.
* '''流程图 Flowchart'''和'''<font color="#ff8000">drakon 图</font>'''，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；
'''<font color="#ff8000">数据流程图 Data-Flow Diagram</font>'''，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 tree]]s, [[protein–protein interaction]] networks, and [[metabolic pathway]]s.{{sfnp|Bachmaier|Brandes|Schreiber|2014}}
*'''数据流程图 Data-Flow Diagram'''，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；
* 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。{{sfnp|Bachmaier|Brandes|Schreiber|2014}}
此外，'''电子设计自动化 electronic design automation（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 distributed computing'''中'''<font color="#ff8000">贪婪嵌入 Greedy embedding</font>'''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==
==软件==
[[File:Gephi 0.9.1 Network Analysis and Visualization Software.png|thumb|
[[File:Gephi 0.9.1 Network Analysis and Visualization Software.png|thumb|图6：A graph drawing interface 一个画图软件界面([[Gephi]] 0.9.1)]]
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:
软件、系统和绘制图形系统的提供者包括:
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 Software|free/libre]] [[Python (programming language)|Python]] library for analysis of graphs.
* Graph-Tool：一个免费/免费的Python库，用于分析图形
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]]<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>
* Graphviz：来自美国电话电报公司的开放源码绘图系统<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]]
* 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.<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>
* 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。<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>
* 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]]<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.
* 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)]],<ref>"Tulip – A Huge Graph Visualization Framework", by David Auber, in {{harvtxt| Jünger|Mutzel|2004}}.</ref> an open source data visualization tool
* [[Tulip (software)]],an open source data visualization tool
Tulip ：<ref>"Tulip – A Huge Graph Visualization Framework", by David Auber, in {{harvtxt| Jünger|Mutzel|2004}}.</ref> 开源数据可视化工具
* [[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>
* yEd 具有图形布局功能的图形编辑器<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>
* PGF/TikZ 带graphdrawing软件包的3.0（需要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
* 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
==参考文献==
==参考文献==
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一般参考资料
===一般参考资料===
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===专门的子主题===
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*{{citation|title=Automata Theory with Modern Applications|first1=James Andrew|last1=Anderson|first2=Thomas J.|last2=Head|publisher=Cambridge University Press|year=2006|isbn=978-0-521-84887-9|pages=38–41|url=https://books.google.com/books?id=ikS8BLdLDxIC&pg=PA38}}.
*{{citation|title=Automata Theory with Modern Applications|first1=James Andrew|last1=Anderson|first2=Thomas J.|last2=Head|publisher=Cambridge University Press|year=2006|isbn=978-0-521-84887-9|pages=38–41|url=https://books.google.com/books?id=ikS8BLdLDxIC&pg=PA38}}.
*{{citation|first1=Christian|last1=Bachmaier|first2=Ulrik|last2=Brandes|first3=Falk|last3=Schreiber|contribution=Biological Networks|pages=621–651|editor-first=Roberto|editor-last=Tamassia|editor-link=Roberto Tamassia|title=Handbook of Graph Drawing and Visualization|publisher=CRC Press|year=2014}}.
*{{citation|first1=Christian|last1=Bachmaier|first2=Ulrik|last2=Brandes|first3=Falk|last3=Schreiber|contribution=Biological Networks|pages=621–651|editor-first=Roberto|editor-last=Tamassia|editor-link=Roberto Tamassia|title=Handbook of Graph Drawing and Visualization|publisher=CRC Press|year=2014}}.
*{{citation|contribution=Layered drawings of digraphs|first1=Oliver|last1=Bastert|first2=Christian|last2=Matuszewski|title=Drawing Graphs: Methods and Models|editor1-first=Michael|editor1-last=Kaufmann|editor2-first=Dorothea|editor2-last=Wagner|editor2-link=Dorothea Wagner|publisher=Springer-Verlag|series=Lecture Notes in Computer Science|volume=2025|year=2001|pages=87–120|doi=10.1007/3-540-44969-8_5|isbn=978-3-540-42062-0}}.
*{{citation|contribution=Layered drawings of digraphs|first1=Oliver|last1=Bastert|first2=Christian|last2=Matuszewski|title=Drawing Graphs: Methods and Models|editor1-first=Michael|editor1-last=Kaufmann|editor2-first=Dorothea|editor2-last=Wagner|editor2-link=Dorothea Wagner|publisher=Springer-Verlag|series=Lecture Notes in Computer Science|volume=2025|year=2001|pages=87–120|doi=10.1007/3-540-44969-8_5|isbn=978-3-540-42062-0}}.
*{{citation | last = Beckman | first = Brian | publisher = Microsoft Research | series = Tech. Report MSR-TR-94-04 | title = Theory of Spectral Graph Layout | url = http://research.microsoft.com/apps/pubs/default.aspx?id=69611 | year = 1994}}.
*{{citation | last = Beckman | first = Brian | publisher = Microsoft Research | series = Tech. Report MSR-TR-94-04 | title = Theory of Spectral Graph Layout | url = http://research.microsoft.com/apps/pubs/default.aspx?id=69611 | year = 1994}}.
*{{citation|first1=Ulrik|last1=Brandes|first2=Linton C.|last2=Freeman|first3=Dorothea|last3=Wagner|author3-link=Dorothea Wagner|contribution=Social Networks|pages=805–839|editor-first=Roberto|editor-last=Tamassia|editor-link=Roberto Tamassia|title=Handbook of Graph Drawing and Visualization|publisher=CRC Press|year=2014}}.
*{{citation|first1=Ulrik|last1=Brandes|first2=Linton C.|last2=Freeman|first3=Dorothea|last3=Wagner|author3-link=Dorothea Wagner|contribution=Social Networks|pages=805–839|editor-first=Roberto|editor-last=Tamassia|editor-link=Roberto Tamassia|title=Handbook of Graph Drawing and Visualization|publisher=CRC Press|year=2014}}.
*{{citation|first1=Giuseppe|last1=Di Battista|first2=Massimo|last2=Rimondini|contribution=Computer Networks|pages=763–803|editor-first=Roberto|editor-last=Tamassia|editor-link=Roberto Tamassia|title=Handbook of Graph Drawing and Visualization|publisher=CRC Press|year=2014}}.
*{{citation|first1=Giuseppe|last1=Di Battista|first2=Massimo|last2=Rimondini|contribution=Computer Networks|pages=763–803|editor-first=Roberto|editor-last=Tamassia|editor-link=Roberto Tamassia|title=Handbook of Graph Drawing and Visualization|publisher=CRC Press|year=2014}}.
*{{citation | last1 = Doğrusöz | first1 = Uğur | last2 = Madden | first2 = Brendan| last3 = Madden | first3 = Patrick | editor-last = North | editor-first = Stephen| contribution = Circular layout in the Graph Layout toolkit | doi = 10.1007/3-540-62495-3_40 | pages = 92–100| publisher = Springer-Verlag | series = Lecture Notes in Computer Science | title = Symposium on Graph Drawing, GD '96 Berkeley, California, USA, September 18–20, 1996, Proceedings | volume = 1190 | year = 1997| isbn = 978-3-540-62495-0 | doi-access = free }}.
*{{citation | last1 = Doğrusöz | first1 = Uğur | last2 = Madden | first2 = Brendan| last3 = Madden | first3 = Patrick | editor-last = North | editor-first = Stephen| contribution = Circular layout in the Graph Layout toolkit | doi = 10.1007/3-540-62495-3_40 | pages = 92–100| publisher = Springer-Verlag | series = Lecture Notes in Computer Science | title = Symposium on Graph Drawing, GD '96 Berkeley, California, USA, September 18–20, 1996, Proceedings | volume = 1190 | year = 1997| isbn = 978-3-540-62495-0 | doi-access = free }}.
*{{citation| last1 = Eiglsperger | first1 = Markus | last2 = Fekete | first2 = Sándor | last3 = Klau | first3 = Gunnar | contribution = Orthogonal graph drawing | doi = 10.1007/3-540-44969-8_6
*{{citation| last1 = Eiglsperger | first1 = Markus | last2 = Fekete | first2 = Sándor | last3 = Klau | first3 = Gunnar | contribution = Orthogonal graph drawing | doi = 10.1007/3-540-44969-8_6
*{{citation | last = Freese | first = Ralph | editor-last = Eklund | editor-first = Peter | contribution = Automated lattice drawing | doi = 10.1007/978-3-540-24651-0_12 | pages = 589–590
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| publisher = Springer-Verlag | series = Lecture Notes in Computer Science | title = Concept Lattices: Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings | url = http://www.math.hawaii.edu/~ralph/Preprints/latdrawing.pdf | volume = 2961 | year = 2004| isbn = 978-3-540-21043-6 | citeseerx = 10.1.1.69.6245 }}.
| publisher = Springer-Verlag | series = Lecture Notes in Computer Science | title = Concept Lattices: Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings | url = http://www.math.hawaii.edu/~ralph/Preprints/latdrawing.pdf | volume = 2961 | year = 2004| isbn = 978-3-540-21043-6 | citeseerx = 10.1.1.69.6245 }}.
*{{citation | last1 = Garg | first1 = Ashim | last2 = Tamassia | first2 = Roberto | doi = 10.1007/BF01108622| issue = 2 | journal = Order | mr = 1354797 | pages = 109–133 | title = Upward planarity testing | volume = 12 | year = 1995| citeseerx = 10.1.1.10.2237 }}.
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*{{citation | last1 = Holten | first1 = Danny | last2 = Isenberg | first2 = Petra | last3 = van Wijk | first3 = Jarke J. | author3-link = Jack van Wijk | last4 = Fekete | first4 = Jean-Daniel
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| last4 = Fekete | first4 = Jean-Daniel | contribution = An extended evaluation of the readability of tapered, animated, and textured directed-edge representations in node-link graphs
| last4 = Fekete | first4 = Jean-Daniel | contribution = An extended evaluation of the readability of tapered, animated, and textured directed-edge representations in node-link graphs
| doi = 10.1109/PACIFICVIS.2011.5742390 | pages = 195–202 | title = IEEE Pacific Visualization Symposium (PacificVis 2011) | url = http://www.lri.fr/~isenberg/publications/papers/Holten_2011_AEP.pdf | year = 2011| isbn = 978-1-61284-935-5 }}.
| doi = 10.1109/PACIFICVIS.2011.5742390 | pages = 195–202 | title = IEEE Pacific Visualization Symposium (PacificVis 2011) | url = http://www.lri.fr/~isenberg/publications/papers/Holten_2011_AEP.pdf | year = 2011| isbn = 978-1-61284-935-5 }}.
*{{citation |last1= Holten |first1 = Danny |last2 = van Wijk |first2= Jarke J. |contribution = A user study on visualizing directed edges in graphs |doi= 10.1145/1518701.1519054
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|pages= 2299–2308 |title= Proceedings of the 27th International Conference on Human Factors in Computing Systems (CHI '09) |url= http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf
|pages= 2299–2308 |title= Proceedings of the 27th International Conference on Human Factors in Computing Systems (CHI '09) |url= http://www.win.tue.nl/~dholten/papers/directed_edges_chi.pdf
*{{citation | last = Koren | first = Yehuda | doi = 10.1016/j.camwa.2004.08.015 | issue = 11–12 | journal = Computers & Mathematics with Applications | mr = 2154691 | pages = 1867–1888 | title = Drawing graphs by eigenvectors: theory and practice | url = https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/DBLP-journals-camwa-Koren05.pdf| volume = 49| year = 2005| access-date = 2011-09-17 | archive-url = https://web.archive.org/web/20120402131402/https://akpublic.research.att.com/areas/visualization/papers_videos/pdf/DBLP-journals-camwa-Koren05.pdf| archive-date = 2012-04-02 | url-status = dead
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*{{citation | last = Longabaugh | first = William | doi = 10.1186/1471-2105-13-275 | journal = BMC Bioinformatics | pages = 275 | title = Combing the hairball with BioFabric: a new approach for visualization of large networks | url = http://www.biomedcentral.com/content/pdf/1471-2105-13-275.pdf| pmid = 23102059| volume = 13| year = 2012| pmc=3574047}}.
*{{citation | last = Longabaugh | first = William | doi = 10.1186/1471-2105-13-275 | journal = BMC Bioinformatics | pages = 275 | title = Combing the hairball with BioFabric: a new approach for visualization of large networks | url = http://www.biomedcentral.com/content/pdf/1471-2105-13-275.pdf| pmid = 23102059| volume = 13| year = 2012| pmc=3574047}}.
*{{citation| last1 = Madden | first1 = Brendan| last2 = Madden | first2 = Patrick| last3 = Powers | first3 = Steve| last4 = Himsolt | first4 = Michael| editor-last = Brandenburg | editor-first = Franz J.| contribution = Portable graph layout and editing| doi = 10.1007/BFb0021822| pages = 385–395 | publisher = Springer-Verlag| series = Lecture Notes in Computer Science| title = Graph Drawing: Symposium on Graph Drawing, GD '95, Passau, Germany, September 20–22, 1995, Proceedings | volume = 1027| year = 1996| title-link = International Symposium on Graph Drawing| isbn = 978-3-540-60723-6| doi-access = free }}.
*{{citation| last1 = Madden | first1 = Brendan| last2 = Madden | first2 = Patrick| last3 = Powers | first3 = Steve| last4 = Himsolt | first4 = Michael| editor-last = Brandenburg | editor-first = Franz J.| contribution = Portable graph layout and editing| doi = 10.1007/BFb0021822| pages = 385–395 | publisher = Springer-Verlag| series = Lecture Notes in Computer Science| title = Graph Drawing: Symposium on Graph Drawing, GD '95, Passau, Germany, September 20–22, 1995, Proceedings | volume = 1027| year = 1996| title-link = International Symposium on Graph Drawing| isbn = 978-3-540-60723-6| doi-access = free }}.
*{{citation | last1 = Misue | first1= K. | last2 = Eades | first2= P.| last3 = Lai | first3 = W.| last4 = Sugiyama | first4 = K. | title = Layout Adjustment and the Mental Map | journal = Journal of Visual Languages and Computing | volume = 6 | number = 2 | pages = 183–210 | year = 1995 | doi=10.1006/jvlc.1995.1010}}.
*{{citation | last1 = Misue | first1= K. | last2 = Eades | first2= P.| last3 = Lai | first3 = W.| last4 = Sugiyama | first4 = K. | title = Layout Adjustment and the Mental Map | journal = Journal of Visual Languages and Computing | volume = 6 | number = 2 | pages = 183–210 | year = 1995 | doi=10.1006/jvlc.1995.1010}}.
*{{citation| last1 = Nachmanson | first1 = Lev | last2 = Robertson | first2 = George| last3 = Lee | first3 = Bongshin| editor1-last = Hong | editor1-first = Seok-Hee | editor2-last = Nishizeki | editor2-first = Takao| editor3-last = Quan | editor3-first = Wu| contribution = Drawing Graphs with GLEE| doi = 10.1007/978-3-540-77537-9_38| pages = 389–394| publisher = Springer-Verlag| series = Lecture Notes in Computer Science| title = Graph Drawing, 15th International Symposium, GD 2007, Sydney, Australia, September 24–26, 2007, Revised Papers| contribution-url = ftp://ftp.research.microsoft.com/pub/TR/TR-2007-72.pdf| volume = 4875| year = 2008|| isbn = 978-3-540-77536-2| doi-access = free }}.
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*{{citation| last1 = Pach | first1 = János | last2 = Sharir | first2 = Micha | contribution = 5.5 Angular resolution and slopes| pages = 126–127| publisher = American Mathematical Society | publisher = American Mathematical Society | series = Mathematical Surveys and Monographs | title = Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures| volume = 152
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| year = 2009}}.
| year = 2009}}.
*{{citation | last1 = Purchase | first1 = H. C. | last2 = Cohen | first2 = R. F. | last3 = James | first3 = M. I. | at = Article 4| doi = 10.1145/264216.264222| journal = Journal of Experimental Algorithmics | title = An experimental study of the basis for graph drawing algorithms| url = https://secure.cs.uvic.ca/twiki/pub/Research/Chisel/ComputationalAestheticsProject/Vol2Nbr4.pdf | volume = 2| year = 1997 }}{{Dead link|date=January 2020 |bot=InternetArchiveBot |fix-attempted=yes }}.
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*{{citation | last = Saaty | first = Thomas L. | journal = Proc. Natl. Acad. Sci. U.S.A. | pages = 688–690 | title = The minimum number of intersections in complete graphs | volume = 52
*{{citation | last = Saaty | first = Thomas L. | journal = Proc. Natl. Acad. Sci. U.S.A. | pages = 688–690 | title = The minimum number of intersections in complete graphs | volume = 52
| volume = 52| issue = 3 | year = 1964 | doi=10.1073/pnas.52.3.688| pmid = 16591215 | pmc = 300329}}.
| volume = 52| issue = 3 | year = 1964 | doi=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|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|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 | doi = 10.7155/jgaa.00301 | issue = 4 | journal = Journal of Graph Algorithms and Applications | pages = 495–513 | title = Graph Drawing in TikZ | volume = 17 | year = 2013}}.
*{{citation | last = Tantau | first = Till | doi = 10.7155/jgaa.00301 | issue = 4 | journal = Journal of Graph Algorithms and Applications | pages = 495–513 | title = Graph Drawing in TikZ | volume = 17 | year = 2013}}.
* {{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}}.
* {{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}}.
* {{dmoz|Science/Math/Combinatorics/Software/Graph_Drawing}} for many additional links related to graph drawing.
* {{dmoz|Science/Math/Combinatorics/Software/Graph_Drawing}} for many additional links related to graph drawing.
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