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{{about|the general subject of graph drawing|the annual research symposium|International Symposium on Graph Drawing}}

{{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.]]

[[File:WorldWideWebAroundWikipedia.png|thumb|

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]]

'''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 [[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.

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.

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.

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。

图形或网络图的绘制是通过从图形抽象出的顶点和边表示的。这个图不应与图形本身混淆: 非常不同的图可以对应于同一个图形。抽象地说，重要的是哪一对顶点是由边连在一起。然而，在具体的绘图中，这些顶点和边的排列影响了它的可理解性、可用性、制造成本和美学。

==Graphical conventions==

==Graphical conventions 画图公约==

[[File:4node-digraph-natural.svg|thumb|upright=0.5|[[Directed graph]] with arrowheads showing edge directions]]

[[File:4node-digraph-natural.svg|thumb|upright=0.5|

图2：[[Directed graph]] with arrowheads showing edge directions 带箭头显示边方向的有向图]]

Graphs are frequently drawn as node–link diagrams in which the vertices are represented as disks, boxes, or textual labels and the edges are represented as [[line 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 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.

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。

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

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

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。

在有向图的情况下，箭头约定俗成的来显示它们的方向; 向上的平面绘图使用以下约定：每个边都从较低的顶点定向到较高的顶点，因此不需要箭头。

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

节点链接图可被其他画图方式替代，包括邻接表示法，如圆填充，其中顶点表示为平面上不相交的区域，边表示为区域之间的邻接; 交点表示，其中顶点由非相交的几何对象表示，而边线由其交点表示；可见性表示，其中顶点由平面中的区域表示，边由彼此无障碍视线的区域表示; 汇流图，其中边表示为数学轨迹上的光滑曲线; 织物，其中顶点表示为水平线，边表示为垂直线; 以及图形邻接矩阵的可视化结点。

==Quality measures==

==Quality measures 质量度量==

Many different quality measures have been defined for graph drawings, in an attempt to find objective means of evaluating their aesthetics and usability.<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.<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.

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.

 

*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 [[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.

*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>

*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.

*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.

*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>

*[[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"/>

*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==

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>]]

[[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:

There are many different graph layout strategies:

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

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:

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>

*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>

*[[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>

*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>

*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>

*[[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]]

[[File:Goldner-Harary-linear.svg|thumb|

图5：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.

*[[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>

*[[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>

*[[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 专用图==

==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

Graphs and graph drawings arising in other areas of application include

Graphs and graph drawings arising in other areas of application include

* [[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>

* [[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>

* [[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}}

* [[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}}

* [[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}}

* [[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.

* [[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.

* [[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}}

* [[Bioinformatics]] including [[phylogenetic tree]]s, [[protein–protein interaction]] networks, and [[metabolic pathway]]s.{{sfnp|Bachmaier|Brandes|Schreiber|2014}}

 

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

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

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

此外，电子设计自动化（EDA）的布局和布线步骤在很多方面与图形绘制相似，而在分布式计算中贪婪嵌入的问题也是如此，并且图形绘制文献包括从EDA文献中借来的一些结果。然而，这些问题也在几个重要方面有所不同: 例如，在 EDA，面积最小化和信号长度比美观更重要，EDA中的路由问题可能每个网有两个以上的终端，而图绘制中的类似问题通常只涉及每条边的顶点对。

==Software==

==Software 软件==

[[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:

[[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)]]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:

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:

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.

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

* [[Cytoscape]], open-source software for visualizing molecular interaction networks

* [[Cytoscape]], open-source software for visualizing molecular interaction networks

* [[Gephi]], open-source network analysis and visualization software

* [[Gephi]], open-source network analysis and visualization software

* [[graph-tool]], a [[Free Software|free/libre]] [[Python (programming language)|Python]] library for analysis of graphs.

* [[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>

* [[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]]

* [[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>

* [[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>

* [[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.

* [[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.

* [[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

* [[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>

* [[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>

* [[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

* [[LaNet-vi]], an open-source large network visualization software

* [[Edraw Max]] 2D business technical diagramming software

* [[Edraw Max]] 2D business technical diagramming software