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TreeGraph

TreeGraph[{v₁,v₂,…},{u₁,u₂,…}]

生成一个树，其中 u_i 是 v_i 的前驱.

TreeGraph[{e₁,e₂,…}]

产生一棵边为 e_j 的树.

TreeGraph[{v₁,v₂,…},{e₁,e₂,…}]

产生一棵顶点为 v_i 边为 e_j 的树.

TreeGraph[{…,w_i[v_i,…],…},{…,w_j[e_j,…],…}]

产生一棵树，其中顶点和边的属性由符号封装 w_k 定义.

TreeGraph[{v_iv_j,…}]

用规则 v_iv_j 指定树.

TreeGraph

TreeGraph[{v₁,v₂,…},{u₁,u₂,…}]

生成一个树，其中 u_i 是 v_i 的前驱.

TreeGraph[{e₁,e₂,…}]

产生一棵边为 e_j 的树.

TreeGraph[{v₁,v₂,…},{e₁,e₂,…}]

产生一棵顶点为 v_i 边为 e_j 的树.

TreeGraph[{…,w_i[v_i,…],…},{…,w_j[e_j,…],…}]

产生一棵树，其中顶点和边的属性由符号封装 w_k 定义.

TreeGraph[{v_iv_j,…}]

用规则 v_iv_j 指定树.

范例

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基本范例 (1)

来自父结点和子结点对的一棵树：

Wolfram Language code: TreeGraph[{12, 13, 14}]

来自顶点和边组成的列表的一棵树：

Wolfram Language code: TreeGraph[{1, 2, 3, 4}, {12, 13, 14}]

范围 (25)

连通性 (6)

使用  符号创建一个无向图；以 ue 输入该符号：

Wolfram Language code: TreeGraph[{12, 13, 14}]

使用  符号创建一个有向图；以 de 输入该符号：

Wolfram Language code: TreeGraph[{12, 13, 14}]

从规则列表创建一个有向图：

Wolfram Language code: TreeGraph[{1 -> 2, 1 -> 3, 1 -> 4}]

从规则列表创建一个无向图：

Wolfram Language code: TreeGraph[{1 -> 2, 1 -> 3, 1 -> 4}, DirectedEdges -> False]

使用 VertexList 和 EdgeList 以获取顶点和边：

Wolfram Language code: {g1, g2} = {TreeGraph[{12, 13, 14}], TreeGraph[{13, 12, 14}]}

边的排序采用输入的顺序：

Wolfram Language code: EdgeList /@ {g1, g2}

顶点的排序采用在边中输入的顺序：

Wolfram Language code: VertexList /@ {g1, g2}

利用显式顶点列表，控制 VertexList 所用的排序：

Wolfram Language code: {g1, g2} = {TreeGraph[{1, 2, 3, 4}, {13, 12, 14}], TreeGraph[{3, 2, 1, 4}, {13, 12, 14}]}

输入顶点列表控制所得的顶点排序：

Wolfram Language code: VertexList /@ {g1, g2}

任意表达式都可用作顶点：

Wolfram Language code:

{TreeGraph[{ab, ac}], TreeGraph[{"foo""bar", "foo""gnu"}], 
	TreeGraph[{[image][image], [image][image]}]}

Wolfram Language code: VertexList /@ %

封装 (5)

在顶点或者边上使用封装：

Wolfram Language code: {TreeGraph[{Style[1, Red], 2, 3, 4}, {12, 13, 14}], TreeGraph[{1, 2, 3, 4}, {Style[12, Red], 13, 14}]}

封装可以嵌套：

Wolfram Language code:

{TreeGraph[{Labeled[Style[1, Red], "hello"], 2, 3, 4}, {12, 13, 14}], TreeGraph[{1, 2, 3, 4}, {Style[Labeled[12, "hello"], Red], 13, 14}]}

通过封装如 Tooltip，添加交互式行为：

Wolfram Language code: TreeGraph[{12, 13, Tooltip[Style[14, Red], "hello"]}]

在工具提示条中，可以使用任意对象：

Wolfram Language code: TreeGraph[{12, 13, Tooltip[Style[14, Red], Plot[Sin[x], {x, 0, 2Pi}]]}]

利用 Button 当点击一条边或者一个顶点时触发动作：

Wolfram Language code:

{TreeGraph[{12, Button[Style[13, Red], Speak["Edge from 1 to 3"]]}], TreeGraph[{1, 2, Button[Style[3, Red], Speak["Vertex 3"]]}, {12, 23}, VertexSize -> Medium]}

利用 PopupWindow 提供进一步的详细信息：

Wolfram Language code: TreeGraph[{12, 13, PopupWindow[Style[14, Red], DateListPlot[FinancialData["IBM", "Jan. 1, 2004"]]]}]

样式化 (8)

对所有顶点或者边设置样式：

Wolfram Language code: {TreeGraph[{12, 13, 14}, VertexStyle -> Green], TreeGraph[{12, 13, 14}, EdgeStyle -> Green]}

使用选项设置单个顶点或者边的样式：

Wolfram Language code:

{TreeGraph[{12, 13, 14}, VertexStyle -> {1 -> Green, Orange}], TreeGraph[{12, 13, 14}, EdgeStyle -> {12 -> Green, Orange}]}

对单个样式使用封装：

Wolfram Language code:

{TreeGraph[{Style[1, Green], 2, 3}, {12, 13, 14}, VertexStyle -> Orange], TreeGraph[{Style[12, Green], 13, 14}, EdgeStyle -> Orange]}

使用符号式尺寸，调整顶点的大小：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, PlotLabel -> s], {s, {Tiny, Small, Medium, Large}}]

或者使用相对于各顶点中心的最小距离的尺寸：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, PlotLabel -> s], {s, {0.1, 0.2, 0.5, 1}}]

使用 VertexShapeFunction 的内置设置：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> s, VertexSize -> 0.2, PlotLabel -> s], {s, {"Triangle", "Square", "Rectangle", "Pentagon", "Hexagon", "Octagon"}}]

圆角形状：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> s, VertexSize -> 0.2, PlotLabel -> s], {s, ResourceData["VertexShapeFunction", "Rounded"]}]

凹形形状：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> s, VertexSize -> 0.2, PlotLabel -> s], {s, ResourceData["VertexShapeFunction", "Concave"]}]

绘制单个顶点：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> { 1 -> "Square"}, VertexSize -> 0.2]

与默认顶点函数联合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> { 1 -> "Square", "Triangle"}, VertexSize -> 0.2]

将任意 Graphics、Image 或者 Graphics3D 作为顶点形状使用：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexShape -> s, VertexSize -> Medium], {s, {[image], [image], [image]}}]

使用 EdgeShapeFunction 的内置设置：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, {"BoxLine", "DiamondLine", "DotLine"}}]

包含实心箭头的有向边：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "FilledArrow"]}]

线型箭头：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "UnfilledArrow"]}]

开放式箭头：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "CarvedArrow"]}]

对单条边指定边函数：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {12 -> "UnfilledArrow"}]

与一个不同的默认边函数联合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {12 -> "FilledArrow", "CarvedArrow"}]

标签 (6)

对任意边或者顶点添加标签：

Wolfram Language code: {TreeGraph[{Labeled[12, "hello"], 13, 14}], TreeGraph[{Labeled[1, "hello"], 2, 3}, {12, 13, 14}]}

将任意表达式作为标签使用：

Wolfram Language code: Table[TreeGraph[{1, 2, Labeled[3, l]}, {12, 13, 14}], {l, {Sin[x], [image], [image]}}]

Wolfram Language code: Table[TreeGraph[{12, 13, Labeled[14, l]}], {l, {Sin[x], [image], [image]}}]

使用 Placed 控制顶点标签的位置，包括位置内的符号：

Wolfram Language code:

Table[TreeGraph[{1, 2, Labeled[3, Placed["■■", p]]}, {12, 23}, PlotLabel -> p, VertexSize -> 0.25, VertexShapeFunction -> "Square"], {p, {Left, Right, Top, Bottom}}]

位置外的符号：

Wolfram Language code:

Table[TreeGraph[{1, 2, Labeled[3, Placed["■■", p]]}, {12, 23}, PlotLabel -> p, VertexSize -> Small, VertexShapeFunction -> "Square"], {p, {Before, After, Below, Above}}]

基于坐标的位置：

Wolfram Language code:

Table[TreeGraph[{1, 2, Labeled[3, Placed["■", p]]}, {12, 13}, VertexSize -> 0.25, VertexShapeFunction -> "Square", PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

使用 Placed 在封装中放置多个标签：

Wolfram Language code: TreeGraph[{1, 2, 3, Labeled[4, Placed[{"lbl1", "lbl2"}, {Above, Below}]]}, {12, 13, 14}]

可以使用任意数目的标签：

Wolfram Language code:

TreeGraph[{1, 2, 3, Labeled[4, Placed[{"lbl1", "lbl2", "lbl3", "lbl4"}, {Above, After, Below, Before}]]}, {12, 13, 14}]

使用 VertexLabels 放置多个标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> {4 -> Placed[{"lbl1", "lbl2"}, {Above, Below}]}]

使用具有符号位置的 Placed 控制边上的标签位置：

Wolfram Language code:

Table[TreeGraph[{Labeled[12, Placed["■■", p]], 13}, PlotLabel -> p, VertexSize -> Small], {p, {"Start", "Middle", "End"}}]

使用显式坐标来放置标签：

Wolfram Language code:

Table[TreeGraph[{Labeled[12, Placed["■■", p]], 13}, PlotLabel -> p, VertexSize -> Small, BaselinePosition -> Bottom], {p, {0, 1 / 4, 1 / 3}}]

使用 Placed 在一个封装内放置多个标签：

Wolfram Language code: TreeGraph[{12, 13, Labeled[14, Placed[{"lbl1", "lbl2"}, {"Start", "End"}]]}]

可以使用任意数目的标签：

Wolfram Language code: TreeGraph[{12, 13, Labeled[14, Placed[{"lbl1", "lbl2", "lbl3"}, {"Start", "Middle", "End"}]]}]

使用 EdgeLabels 放置多个标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeLabels -> {14 -> Placed[{"lbl1", "lbl2"}, {"Start", "End"}]}]

选项 (82)

AnnotationRules (3)

指定顶点的注解：

Wolfram Language code: TreeGraph[{12, 13, 14}, AnnotationRules -> {1 -> {VertexLabels -> "hello"}}]

边：

Wolfram Language code: TreeGraph[{12, 13, 14}, AnnotationRules -> {12 -> {EdgeLabels -> "hello"}}]

图自身：

Wolfram Language code: TreeGraph[{12, 13, 14}, AnnotationRules -> {"GraphProperties" -> {"Message" -> "hello"}}]

Wolfram Language code: AnnotationValue[%, "Message"]

DirectedEdges (2)

默认情况下，如果给出的是一个规则列表，将产生有向树：

Wolfram Language code: TreeGraph[{1 -> 2, 1 -> 3, 1 -> 4}, EdgeStyle -> Arrowheads[Medium], EdgeShapeFunction -> "Arrow"]

使用 DirectedEdges->False 将规则解释为无向边：

Wolfram Language code: TreeGraph[{1 -> 2, 1 -> 3, 1 -> 4}, DirectedEdges -> False]

使用 DirectedEdge 或 UndirectedEdge 来直接指定图是有向还是无向：

Wolfram Language code:

{TreeGraph[{12, 13, 14}, EdgeStyle -> Arrowheads[Medium], EdgeShapeFunction -> "Arrow"], TreeGraph[{12, 13, 14}]}

EdgeLabels (7)

对 12 添加标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeLabels -> {12 -> "Hello"}]

为所有边添加标签：

Wolfram Language code: el = {12, 13, 14};

Wolfram Language code: TreeGraph[el, EdgeLabels -> Table[el[[i]] -> Subscript["e", i], {i, Length[el]}]]

将任意表达式用作标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeLabels -> {12 -> [image], 13 -> [image], 14 -> [image]}]

使用具有符号位置信息的 Placed 来控制边上标签的位置：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeLabels -> {12 -> Placed["■■■", p]}, PlotLabel -> p], {p, {"Start", "Middle", "End"}}]

使用显式坐标来放置标签：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeLabels -> {12 -> Placed["■■■", p]}, PlotLabel -> p, BaselinePosition -> Bottom], {p, {0, 1 / 3, 1 / 4}}]

在标签内变化位置：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeLabels -> {12 -> Placed["■■■", {1 / 2, p}]}, PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

将 Placed 用于封装内以放置多个标签：

Wolfram Language code: TreeGraph[{12, 13, Labeled[14, Placed[{"lbl1", "lbl2"}, {"Start", "End"}]]}]

可以使用任意数目的标签：

Wolfram Language code: TreeGraph[{12, 13, Labeled[14, Placed[{"lbl1", "lbl2", "lbl3"}, {"Start", "Middle", "End"}]]}]

使用 EdgeLabels 放置多个标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeLabels -> {14 -> Placed[{"lbl1", "lbl2"}, {"Start", "End"}]}]

通过 Tooltip 和 StatusArea 的值来使用自动标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeLabels -> Placed["Name", Tooltip]]

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeLabels -> Placed["Name", StatusArea]]

EdgeShapeFunction (6)

得到 EdgeShapeFunction 的内置设置列表：

Wolfram Language code: ResourceData["EdgeShapeFunction"]

包括基线的无向边：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeShapeFunction -> "Line"]

边上具有不同图像字符的直线：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, {"BoxLine", "DiamondLine", "DotLine"}}]

包括实心箭头的有向边：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "FilledArrow"]}]

线形箭头：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "UnfilledArrow"]}]

开放式箭头：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "CarvedArrow"]}]

指定单条边的边函数：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {12 -> "FilledArcArrow"}]

与一个不同的默认边函数联合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeShapeFunction -> {12 -> "FilledArcArrow", "CarvedArrow"}]

通过运行程序绘制边：

Wolfram Language code:

ef[pts_List, e_] := 
	Block[{s = 0.015, g = [image]}, {Arrowheads[{{s, 0.33, g}, {s, 0.67, g}}], Arrow[pts]}]

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeShapeFunction -> ef]

EdgeShapeFunction 可以与 EdgeStyle 组合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeStyle -> Blue, EdgeShapeFunction -> (Line[#1]&)]

EdgeShapeFunction 具有比 EdgeStyle 更高的优先级：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeStyle -> Blue, EdgeShapeFunction -> ({Red, Line[#1]}&)]

EdgeStyle (2)

对所有边进行样式化处理：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, EdgeStyle -> style, PlotLabel -> style], {style, {Gray, Dashed, Thick}}]

样式化单条边：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeStyle -> {12 -> Blue, 13 -> Dashed}]

EdgeWeight (2)

为所有边指定权值：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeWeight -> RandomInteger[5, 3]]

Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

将任意数值表达式用作权值：

Wolfram Language code: TreeGraph[{12, 13, 14}, EdgeWeight -> {a, b, c}]

Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

GraphHighlight (3)

突出显示顶点 1：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> Medium, GraphHighlight -> {1}]

突出显示边 13：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> Tiny, GraphHighlight -> {13}]

突出显示顶点和边：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> Tiny, GraphHighlight -> {1, 2, 12, 13}]

GraphHighlightStyle (2)

获取 GraphHighlightStyle 的内置设置列表：

Wolfram Language code: ResourceData["GraphHighlightStyle"]

使用 GraphHighlightStyle 的内置设置：

Wolfram Language code:

TreeGraph[{12, 13, 14}, GraphHighlight -> {1, 13}, VertexSize -> Small, GraphHighlightStyle -> #, PlotLabel -> #]& /@ Select[ResourceData["GraphHighlightStyle"], # =!= Automatic&]

GraphLayout (5)

默认情况下，自动选择布局：

Wolfram Language code: TreeGraph[{12, 13, 14}, GraphLayout -> Automatic]

指定特殊曲线上的布局：

Wolfram Language code:

Table[TreeGraph[Table[ii + 1, {i, 20}], GraphLayout -> l, PlotLabel -> l], {l, {"CircularEmbedding", "SpiralEmbedding"}}]

指定满足最优化标准的布局：

Wolfram Language code: el = EdgeList@CompleteKaryTree[4, 5];

Wolfram Language code:

Table[TreeGraph[el, GraphLayout -> l, PlotLabel -> l], {l, {"SpringEmbedding", "SpringElectricalEmbedding", "HighDimensionalEmbedding"}}]

VertexCoordinates 覆盖 GraphLayout 坐标：

Wolfram Language code:

{TreeGraph[{12, 13, 14}, GraphLayout -> "SpringElectricalEmbedding"], 
	TreeGraph[{12, 13, 14}, GraphLayout -> "SpringElectricalEmbedding", VertexCoordinates -> Table[{i, i}, {i, 0, 3}]]}

利用 AbsoluteOptions 来提取使用一个布局算法计算得到的 VertexCoordinates：

Wolfram Language code: TreeGraph[{12, 13, 14}]

Wolfram Language code: AbsoluteOptions[%, VertexCoordinates]

PlotTheme (4)

基本主题 (2)

使用普通基本主题：

Wolfram Language code: TreeGraph[{12, 13, 14}, PlotTheme -> "Business"]

使用单色主题：

Wolfram Language code: TreeGraph[{12, 13, 14}, PlotTheme -> "Monochrome"]

特色主题 (2)

使用大型图主题：

Wolfram Language code: TreeGraph[{12, 13, 14}, PlotTheme -> "LargeGraph"]

使用经典图表主题：

Wolfram Language code: TreeGraph[{12, 13, 14}, PlotTheme -> "ClassicDiagram"]

VertexCoordinates (3)

默认情况下，自动计算任意顶点坐标：

Wolfram Language code: TreeGraph[{12, 13, 14}]

使用 AbsoluteOptions 提取所得的顶点坐标：

Wolfram Language code: AbsoluteOptions[%, VertexCoordinates]

指定沿着一个椭圆的布局函数：

Wolfram Language code: ellipseLayout[n_, {a_, b_}] := Table[{a Cos[2Pi / n u], b Sin[2Pi / n u]}, {u, 1, n}]

Wolfram Language code: Graphics[Point[ellipseLayout[20, {2, 1}]]]

使用它来生成图的顶点坐标：

Wolfram Language code: TreeGraph[Table[1i, {i, 2, 20}], VertexCoordinates -> ellipseLayout[20, {2, 1}]]

VertexCoordinates 具有比 GraphLayout 更高的优先级：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexCoordinates -> Table[{i, i}, {i, 4}], GraphLayout -> "CircularEmbedding"]

VertexLabels (13)

将顶点名称用作标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> "Name"]

对单个顶点添加标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> {2 -> "one"}]

对所有顶点添加标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> Table[i -> Subscript[v, i], {i, 4}]]

将任意表达式用作标签：

Wolfram Language code: TreeGraph[{12, 13}, VertexLabels -> {1 -> [image], 2 -> [image], 3 -> [image]}, ImagePadding -> 30]

使用具有符号位置信息的 Placed 来控制标签位置，包括外部位置：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> 0.1, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 4}], PlotLabel -> p], {p, {Before, After, Below, Above}}]

拐角外的符号表示：

Wolfram Language code: pl = {{Before, Below}, {After, Below}, {Before, Above}, {After, Above}};

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> 0.1, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 4}], PlotLabel -> p], {p, pl}]

位置内的符号表示：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> 0.35, VertexLabels -> Table[i -> Placed["■■■", p], {i, 4}], VertexShapeFunction -> "Square", PlotLabel -> p], {p, {Left, Top, Right, Bottom}}]

拐角内的符号表示：

Wolfram Language code: pl = {{Left, Bottom}, {Right, Bottom}, {Left, Top}, {Right, Top}};

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> 0.35, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 4}], PlotLabel -> p], {p, pl}]

利用显式坐标放置标签的中心：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> 0.25, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed[[image], p], {i, 4}], PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

把所有标签放在顶点的右上角，并且改变标签内的坐标：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> 0.35, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed[[image], {{1, 1}, p}], {i, 4}], PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

将 Placed 用于封装内以放置多个标签：

Wolfram Language code: TreeGraph[{1, 2, 3, Labeled[4, Placed[{"lbl1", "lbl2"}, {Above, Below}]]}, {12, 13, 14}]

可以使用任意数目的标签：

Wolfram Language code:

TreeGraph[{1, 2, 3, Labeled[4, Placed[{"lbl1", "lbl2", "lbl3", "lbl4"}, {Above, After, Below, Before}]]}, {12, 13, 14}]

使用 VertexLabels 放置多个标签：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> {4 -> Placed[{"lbl1", "lbl2"}, {Above, Below}]}]

使用 Placed 的变量来控制格式化，包括 Tooltip：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> Placed["Name", Tooltip]]

或者 StatusArea：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> Placed["Name", StatusArea]]

使用更精密的格式化函数：

Wolfram Language code: rotateLabel[lab_] := Rotate[lab, 45Degree]

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> Table[i -> Placed["xxx", Below, rotateLabel], {i, 4}]]

Wolfram Language code: panelLabel[lab_] := Panel[lab, FrameMargins -> 0, Background -> Lighter[Yellow, 0.7]]

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> Table[i -> Placed["xxx", Center, panelLabel], {i, 4}]]

Wolfram Language code: hyperlinkLabel[lab_] := Hyperlink[lab, "http://www.wolfram.com"]

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexLabels -> Table[i -> Placed["xxx", Center, hyperlinkLabel], {i, 4}]]

VertexShape (5)

使用任意的 Graphics、Image 或 Graphics3D 作为顶点形状：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexShape -> s, VertexSize -> 0.3], {s, {[image], [image], [image]}}]

指定单个顶点的形状：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShape -> {2 -> [image]}, VertexSize -> 0.3]

VertexShape 可与 VertexSize 组合使用：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, VertexShape -> [image], PlotLabel -> s], {s, {Medium, Large}}]

VertexShape 不受 VertexStyle 的影响：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.3, VertexShape -> [image], VertexStyle -> Blue]

VertexShapeFunction 具有比 VertexShape 更高的优先级：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.2, VertexShapeFunction -> "Square", VertexShape -> [image]]

VertexShapeFunction (10)

获取 VertexShapeFunction 一组内置设置的列表：

Wolfram Language code: ResourceData["VertexShapeFunction"]

使用 "Basic" 系列中 VertexShapeFunction 的内置设置：

Wolfram Language code: ResourceData["VertexShapeFunction", "Basic"]

简单基本形状：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, {"Triangle", "Square", "Rectangle", "Pentagon", "Hexagon", "Octagon"}}]

普通基本形状：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, {"DownTrapezoid", "UpTrapezoid", "Parallelogram", "FiveDown", "Circle", "Diamond", "Star", "Capsule"}}]

使用 "Rounded" 系列中 VertexShapeFunction 的内置设置：

Wolfram Language code: ResourceData["VertexShapeFunction", "Rounded"]

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, ResourceData["VertexShapeFunction", "Rounded"]}]

使用 "Concave" 系列中 VertexShapeFunction 的内置设置：

Wolfram Language code: ResourceData["VertexShapeFunction", "Concave"]

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, ResourceData["VertexShapeFunction", "Concave"]}]

绘制单个顶点：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> { 1 -> "Square"}, VertexSize -> 0.2]

与默认顶点函数组合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> { 1 -> "Square", "Triangle"}, VertexSize -> 0.2]

使用预定义的图形绘制顶点：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> (Inset[[image], #]&)]

通过运行程序来绘制顶点：

Wolfram Language code:

vf[{xc_, yc_}, name_, {w_, h_}] := 
	Block[{xmin = xc - w, xmax = xc + w, ymin = yc - h, ymax = yc + h}, 
	Polygon[{{xmin, ymin}, {xmax, ymax}, {xmin, ymax}, {xmax, ymin}}]
	];

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> vf, VertexSize -> 0.2]

VertexShapeFunction 可以与 VertexStyle 组合使用：

Wolfram Language code: vf1[{xc_, yc_}, name_, {w_, h_}] := Rectangle[{xc - w, yc - h}, {xc + w, yc + h}]

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf1]

VertexShapeFunction 具有比 VertexStyle 更高的优先级：

Wolfram Language code: vf2[{xc_, yc_}, name_, {w_, h_}] := {Red, Rectangle[{xc - w, yc - h}, {xc + w, yc + h}]}

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexShapeFunction 可以与 VertexSize 组合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexShapeFunction -> "Star", VertexSize -> {1 -> Small, Medium}]

VertexShapeFunction 具有比 VertexShape 更高的优先级：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.3, VertexShapeFunction -> "Star", VertexShape -> [image]]

VertexSize (8)

默认情况下，自动计算顶点尺寸：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> Automatic]

使用符号式顶点尺寸，指定所有顶点的大小：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, PlotLabel -> s], {s, {Tiny, Small, Medium, Large}}]

使用顶点坐标之间的最小距离的百分数：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, PlotLabel -> s], {s, 0.1, 1, 0.3}]

使用所有顶点坐标的整体对角线的百分数：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> {"Scaled", s}, PlotLabel -> {"Scaled", s}], {s, 0.1, 1, 0.3}]

指定在和方向上的大小：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, PlotLabel -> s], {s, {{0.1, 0.2}, {0.2, 0.1}}}]

指定单个顶点的大小：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> {1 -> 0.2, 2 -> 0.3}]

VertexSize 可以与 VertexShapeFunction 组合使用：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexSize -> s, VertexShapeFunction -> "Square", PlotLabel -> s], {s, {0.05, 0.1, 0.2}}]

VertexSize 可以与 VertexShape 组合使用：

Wolfram Language code: Table[TreeGraph[{12, 13, 14}, VertexSize -> s, VertexShape -> [image], PlotLabel -> s], {s, {0.1, 0.2, 0.4}}]

VertexStyle (5)

样式化所有顶点：

Wolfram Language code:

Table[TreeGraph[{12, 13, 14}, VertexStyle -> style, VertexSize -> 0.3, PlotLabel -> style], {style, {Yellow, EdgeForm[Dashed]}}]

样式化单个顶点：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexStyle -> {1 -> Blue, 2 -> Red}, VertexSize -> 0.2]

VertexShapeFunction 可以与 VertexStyle 组合使用：

Wolfram Language code: vf1[{xc_, yc_}, name_, {w_, h_}] := Rectangle[{xc - w, yc - h}, {xc + w, yc + h}]

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf1]

VertexShapeFunction 具有比 VertexStyle 更高的优先级：

Wolfram Language code: vf2[{xc_, yc_}, name_, {w_, h_}] := {Red, Rectangle[{xc - w, yc - h}, {xc + w, yc + h}]}

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexStyle 可以与 BaseStyle 组合使用：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexStyle -> LightBlue, BaseStyle -> EdgeForm[Dotted], VertexSize -> 0.2]

VertexStyle 具有比 BaseStyle 更高的优先级：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexStyle -> LightBlue, BaseStyle -> Gray, VertexSize -> 0.2]

VertexShape 不受 VertexStyle 的影响：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexSize -> 0.3, VertexShape -> [image], VertexStyle -> Blue]

VertexWeight (2)

设置所有顶点的权值：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexWeight -> {2, 3, 4, 5}]

Wolfram Language code: AnnotationValue[{%, 1}, VertexWeight]

使用任何数值表达式作为权值：

Wolfram Language code: TreeGraph[{12, 13, 14}, VertexWeight -> {a, b, c, d}]

Wolfram Language code: AnnotationValue[{%, 1}, VertexWeight]

应用 (4)

生成一个随机树：

Wolfram Language code: g = TreeGraph[RandomInteger[#]  # + 1 & /@ Range[0, 30], VertexSize -> 0.4]

突出显示 GraphCenter 和 GraphPeriphery：

Wolfram Language code: {HighlightGraph[g, GraphCenter[g]], HighlightGraph[g, GraphPeriphery[g]]}

VertexEccentricity：

Wolfram Language code: g = TreeGraph[RandomInteger[#]  # + 1 & /@ Range[0, 30], VertexSize -> 0.4];

Wolfram Language code: VertexEccentricity[g, #]& /@ Range[3]

突出显示顶点离心率路径：

Wolfram Language code:

FindVertexEccentricityPath[g_ ? UndirectedGraphQ, u_] /; MemberQ[VertexList[g], u] := Module[{d = GraphDistanceMatrix[g], posu, posv, vl = VertexList[g]}, posu = VertexIndex[g, u];
	posv = First@First@Position[d[[posu]], Max[d[[posu]]]];
	PathGraph[FindShortestPath[g, u, vl[[posv]]]]]

Wolfram Language code: Table[HighlightGraph[g, FindVertexEccentricityPath[g, u]], {u, Range[3]}]

GraphRadius：

Wolfram Language code: g = TreeGraph[RandomInteger[#]  # + 1 & /@ Range[0, 30], VertexSize -> 0.4];

Wolfram Language code: GraphRadius[g]

突出显示半径路径：

Wolfram Language code:

FindRadiusPath[g_ ? UndirectedGraphQ] := Module[{c = First@GraphCenter[g], d, v, pos}, d = Table[GraphDistance[g, c, u], {u, VertexList[g]}];
	pos = First@Position[d, Max[d]];
	v = First@Part[VertexList[g], pos];
	PathGraph[FindShortestPath[g, c, v]]]

Wolfram Language code: HighlightGraph[g, FindRadiusPath[g]]

GraphDiameter：

Wolfram Language code: g = TreeGraph[RandomInteger[#]  # + 1 & /@ Range[0, 30], VertexSize -> 0.4];

Wolfram Language code: GraphDiameter[g]

突出显示直径路径：

Wolfram Language code:

FindDiameterPath[g_ ? UndirectedGraphQ] := Module[{d = GraphDistanceMatrix[g], u, v, pos}, pos = First@Position[d, Max[d]];
	{u, v} = Part[VertexList[g], pos];
	PathGraph[FindShortestPath[g, u, v]]]

Wolfram Language code: HighlightGraph[g, FindDiameterPath[g]]

属性和关系 (9)

使用 VertexCount 和 EdgeCount 计算顶点数和边数：

Wolfram Language code: g = CompleteKaryTree[3, 3]

Wolfram Language code: {VertexCount[g], EdgeCount[g]}

使用 VertexList 和 EdgeList 以标准顺序列举顶点和边：

Wolfram Language code: g = TreeGraph[{12, 13, 34}];

Wolfram Language code: {VertexList[g], EdgeList[g]}

边和顶点以输入时的顺序给出：

Wolfram Language code: g1 = TreeGraph[{34, 12, 13}];

Wolfram Language code: {VertexList[g1], EdgeList[g1]}

从一个图计算 AdjacencyMatrix：

Wolfram Language code: g = TreeGraph[{12, 13, 1 -> 4}, EdgeStyle -> Arrowheads[Medium], EdgeShapeFunction -> "Arrow"]

Wolfram Language code: (a = AdjacencyMatrix[g]//Normal)//MatrixForm

一个树图是连通的：

Wolfram Language code: CompleteKaryTree[3, 3]

Wolfram Language code: {ConnectedGraphQ[%], TreeGraphQ[%]}

树图没有任何环或圈：

Wolfram Language code: TreeGraph[Range[8], {1, 1, 2, 1, 4, 2, 3, 1}]

Wolfram Language code: {LoopFreeGraphQ[%], AcyclicGraphQ[%], TreeGraphQ[%]}

具有个顶点的一个树图具有条边：

Wolfram Language code: TreeGraph[{1 -> 2, 1 -> 3, 2 -> 4, 2 -> 5, 3 -> 6}]

Wolfram Language code: VertexCount[%] - EdgeCount[%]

树图是二分图：

Wolfram Language code: CompleteKaryTree[3, 3]

Wolfram Language code: { TreeGraphQ[%], BipartiteGraphQ[%]}

具有 () 个顶点树图具有至少2个、至多个度数为1的顶点：

Wolfram Language code: TreeGraph[{1 -> 2, 1 -> 3}]

Wolfram Language code: VertexDegree[%]

Wolfram Language code: CompleteKaryTree[2, 6]

Wolfram Language code: VertexDegree[%]

星图是树图：

Wolfram Language code: StarGraph[10]

Wolfram Language code: TreeGraphQ[%]

Top

AlignmentPoint	Center	在图形内对齐的缺省点
AnnotationRules	{}	图、边和顶点的注释
AspectRatio	Automatic	高与宽的比
Axes	False	是否绘制轴
AxesLabel	None	坐标轴标签
AxesOrigin	Automatic	坐标轴原点
AxesStyle	{}	坐标轴样式指定
Background	None	绘图的背景色
BaselinePosition	Automatic	如何与环绕文本基线对齐
BaseStyle	{}	图形的基本样式指定
ContentSelectable	Automatic	是否允许进行内容选择
CoordinatesToolOptions	Automatic	坐标工具的详细行为
DirectedEdges	Automatic	是否将 Rule 解释为 DirectedEdge
EdgeLabels	None	边的标签和标签放置
EdgeLabelStyle	Automatic	边的标签所使用的样式
EdgeShapeFunction	Automatic	如何生成边的图形表示
EdgeStyle	Automatic	边的样式
EdgeWeight	Automatic	边的权值
Epilog	{}	主图形之后执行的图形指令
FormatType	TraditionalForm	文本的缺省样式类型
Frame	False	是否在图形周围放置边框
FrameLabel	None	边框标签
FrameStyle	{}	边框的样式指定
FrameTicks	Automatic	边框刻度
FrameTicksStyle	{}	边框刻度的样式指定
GraphHighlight	{}	要突出显示的图的元素
GraphHighlightStyle	Automatic	突出显示时使用的样式
GraphLayout	Automatic	如何设计顶点和边的布局
GridLines	None	绘制的网格线
GridLinesStyle	{}	网格线的样式指定
ImageMargins	0.	图形周围的边幅
ImagePadding	All	为标签等额外填充内容
ImageSize	Automatic	图形的绝对尺寸
LabelStyle	{}	标签的样式指定
Method	Automatic	使用图形方式的细节
PerformanceGoal	Automatic	优化的目标
PlotLabel	None	图形的一个整体标签
PlotRange	All	图形值的范围
PlotRangeClipping	False	是否在图形范围剪切
PlotRangePadding	Automatic	填充图形值范围的程度
PlotRegion	Automatic	填充的最后显示区域
PlotTheme	$PlotTheme	图的整体主题样式
PreserveImageOptions	Automatic	当显示相同图形的新版本时，是否保存图形选项
Prolog	{}	主图形之前执行的图形指令
RotateLabel	True	是否在边框上旋转 y 标签
Ticks	Automatic	坐标轴标记
TicksStyle	{}	坐标轴标记的样式指定
VertexCoordinates	Automatic	顶点的坐标
VertexLabels	None	顶点的标签和位置
VertexLabelStyle	Automatic	顶点的标签所使用的样式
VertexShape	Automatic	顶点的形状
VertexShapeFunction	Automatic	生成顶点的形状的函数
VertexSize	Medium	顶点的大小
VertexStyle	Automatic	顶点的样式
VertexWeight	Automatic	顶点的权值

TreeGraph

更多信息和选项

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范例

基本范例 (1)

范围 (25)

连通性 (6)

封装 (5)

样式化 (8)

标签 (6)

选项 (82)

AnnotationRules (3)

DirectedEdges (2)

EdgeLabels (7)

EdgeShapeFunction (6)

EdgeStyle (2)

EdgeWeight (2)

GraphHighlight (3)

GraphHighlightStyle (2)

GraphLayout (5)

PlotTheme (4)

基本主题 (2)

特色主题 (2)

VertexCoordinates (3)

VertexLabels (13)

VertexShape (5)

VertexShapeFunction (10)

VertexSize (8)

VertexStyle (5)

VertexWeight (2)

应用 (4)

属性和关系 (9)

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