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PathGraph

PathGraph[{v₁,v₂,…}]

产生一个顶点为 v_i 边在 v_i 和 v_i+1 之间的路径.

PathGraph[{e₁,e₂,…}]

产生一个边为 e_j 的路径.

PathGraph[{v₁,v₂,…},{e₁,e₂,…}]

产生一个顶点为 v_i 边为 e_j 的路径.

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

产生一个顶点和边的属性由符号封装 w_k 定义的路径.

PathGraph[{v_iv_j,…}]

用规则 v_i->v_j 指定路径.

PathGraph

PathGraph[{v₁,v₂,…}]

产生一个顶点为 v_i 边在 v_i 和 v_i+1 之间的路径.

PathGraph[{e₁,e₂,…}]

产生一个边为 e_j 的路径.

PathGraph[{v₁,v₂,…},{e₁,e₂,…}]

产生一个顶点为 v_i 边为 e_j 的路径.

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

产生一个顶点和边的属性由符号封装 w_k 定义的路径.

PathGraph[{v_iv_j,…}]

用规则 v_i->v_j 指定路径.

范例

打开所有单元关闭所有单元

基本范例 (2)

从一个顶点列表构建一个路径：

Wolfram Language code: PathGraph[{a, b, c}]

Wolfram Language code: PathGraph[Range[25]]

边列表：

Wolfram Language code: PathGraph[Table[ii + 1, {i, 20}]]

范围 (6)

连通性 (6)

使用  字符创建一个无向图，按 ue 输入字符：

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

使用  字符创建一个有向图，按 de 输入字符：

Wolfram Language code: PathGraph[{12, 23, 34}, EdgeStyle -> Arrowheads[Medium]]

从规则列表中创建一个有向图：

Wolfram Language code: PathGraph[{1 -> 2, 2 -> 3, 3 -> 4}, EdgeStyle -> Arrowheads[Medium]]

从规则列表中创建一个无向图：

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

使用 VertexList 和 EdgeList 获得顶点和边：

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

边的顺序是它们输入的顺序：

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

顶点的顺序是它们在边中输入的顺序：

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

使用显式顶点列表控制由 VertexList 使用的顺序：

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

输入顶点列表控制结果顶点顺序：

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

任何表达式可以用作顶点：

Wolfram Language code:

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

Wolfram Language code: VertexList /@ %

选项 (82)

AnnotationRules (3)

指定顶点的注释：

Wolfram Language code: PathGraph[Range[5], AnnotationRules -> {1 -> {VertexLabels -> "hello"}}]

边：

Wolfram Language code: PathGraph[Range[5], AnnotationRules -> {12 -> {EdgeLabels -> "hello"}}]

图自身：

Wolfram Language code: PathGraph[Range[5], AnnotationRules -> {"GraphProperties" -> {"Message" -> "hello"}}]

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

DirectedEdges (2)

默认情况下，通过给出边列表生成一个有向图：

Wolfram Language code: PathGraph[{1 -> 2, 2 -> 3, 3 -> 4}, EdgeStyle -> Arrowheads[Medium]]

使用 DirectedEdges->False 将规则解释为无向边：

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

使用 DirectedEdge 或者 UndirectedEdge 直接指定一个图是有向图或者无向图：

Wolfram Language code: {PathGraph[{12, 23, 34}, EdgeStyle -> Arrowheads[Medium]], PathGraph[{12, 23, 34}]}

EdgeLabels (7)

对边 12 添加标签：

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

对所有边分别添加标签：

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

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

将任意表达式作为标签使用：

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

使用具有符号位置信息的 Placed 来控制边上的标签位置：

Wolfram Language code:

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

使用显式坐标放置标签：

Wolfram Language code:

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

改变标签内的位置：

Wolfram Language code:

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

使用 Placed 在一个封装中放置多个标签：

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

可以使用任意数目的标签：

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

使用 EdgeLabels 放置多个标签：

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

通过 Tooltip 和 StatusArea 的值使用多个标签：

Wolfram Language code: PathGraph[Range[4], EdgeLabels -> Placed["Name", Tooltip]]

Wolfram Language code: PathGraph[Range[4], EdgeLabels -> Placed["Name", StatusArea]]

EdgeShapeFunction (6)

获得 EdgeShapeFunction 的内置设置列表：

Wolfram Language code: ResourceData["EdgeShapeFunction"]

无向边包括基本线条：

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

在边上具有不同的符号：

Wolfram Language code:

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

有向边包括固体箭头：

Wolfram Language code:

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

线箭头：

Wolfram Language code:

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

打开箭头：

Wolfram Language code:

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

为单条边指定边函数：

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

组合不同默认边函数：

Wolfram Language code: PathGraph[{12, 23, 3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: PathGraph[Range[4], EdgeShapeFunction -> ef]

EdgeShapeFunction 可以与 EdgeStyle 组合使用：

Wolfram Language code: PathGraph[Range[4], EdgeStyle -> Blue, EdgeShapeFunction -> (Line[#1]&)]

EdgeShapeFunction 比 EdgeStyle 具有更高的优先级：

Wolfram Language code: PathGraph[Range[4], EdgeStyle -> Blue, EdgeShapeFunction -> ({Red, Line[#1]}&)]

EdgeStyle (2)

对所有边进行样式化处理：

Wolfram Language code: Table[PathGraph[Range[10], EdgeStyle -> style, PlotLabel -> style], {style, {Gray, Dashed, Thick}}]

对单条边进行样式化处理：

Wolfram Language code: PathGraph[Range[5], EdgeStyle -> {12 -> Blue, 23 -> Dashed}]

EdgeWeight (2)

指定所有边的权值：

Wolfram Language code: PathGraph[Range[4], EdgeWeight -> RandomInteger[5, 3]]

Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

使用任意数值表达式作为权值：

Wolfram Language code: PathGraph[Range[4], EdgeWeight -> {a, b, c}]

Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

GraphHighlight (3)

突出显示顶点 1：

Wolfram Language code: PathGraph[Range[5], VertexSize -> Medium, GraphHighlight -> {1}]

突出显示边 23：

Wolfram Language code: PathGraph[Range[5], VertexSize -> Tiny, GraphHighlight -> {23}]

突出显示顶点和边：

Wolfram Language code: PathGraph[Range[5], VertexSize -> Tiny, GraphHighlight -> {1, 2, 12, 34}]

GraphHighlightStyle (2)

获得 GraphHighlightStyle 的内置设置列表：

Wolfram Language code: ResourceData["GraphHighlightStyle"]

使用 GraphHighlightStyle 的内置设置：

Wolfram Language code:

PathGraph[Range[20], GraphHighlight -> {1, 2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: PathGraph[Range[10], GraphLayout -> Automatic]

指定特殊曲线上的布局：

Wolfram Language code: Table[PathGraph[Range[20], GraphLayout -> l, PlotLabel -> l], {l, {"CircularEmbedding", "SpiralEmbedding"}}]

指定满足最优化标准的布局：

Wolfram Language code:

Table[PathGraph[Range[20], GraphLayout -> l, PlotLabel -> l], {l, {"SpringEmbedding", "SpringElectricalEmbedding", "HighDimensionalEmbedding"}}]

VertexCoordinates 覆盖 GraphLayout 坐标：

Wolfram Language code:

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

使用 AbsoluteOptions 来提取通过布局算法计算得到的 VertexCoordinates：

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

Wolfram Language code: AbsoluteOptions[%, VertexCoordinates]

PlotTheme (4)

基本主题 (2)

使用常见基本主题样式：

Wolfram Language code: PathGraph[Range[20], PlotTheme -> "Business"]

使用单色主题：

Wolfram Language code: PathGraph[Range[20], PlotTheme -> "Monochrome"]

特色主题 (2)

使用大图主题样式：

Wolfram Language code: PathGraph[Range[20], PlotTheme -> "LargeGraph"]

使用经典示意图主题样式：

Wolfram Language code: PathGraph[Range[20], PlotTheme -> "ClassicDiagram"]

VertexCoordinates (3)

默认情况下，自动计算任意顶点坐标：

Wolfram Language code: PathGraph[Range[4]]

使用 AbsoluteOptions 提取所得的顶点坐标：

Wolfram Language code: AbsoluteOptions[%, VertexCoordinates]

指定一个椭圆上的布局函数：

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: PathGraph[Range[20], VertexCoordinates -> ellipseLayout[20, {2, 1}]]

VertexCoordinates 具有比 GraphLayout 更高的优先级：

Wolfram Language code: PathGraph[Range[4], VertexCoordinates -> Table[{i, i}, {i, 4}], GraphLayout -> "CircularEmbedding"]

VertexLabels (13)

使用顶点名称作为标签：

Wolfram Language code: PathGraph[Range[4], VertexLabels -> "Name"]

对单个顶点添加标签：

Wolfram Language code: PathGraph[Range[4], VertexLabels -> {2 -> "one"}]

对所有顶点添加标签：

Wolfram Language code: PathGraph[Range[4], VertexLabels -> Table[i -> Subscript[v, i], {i, 4}]]

使用任意表达式作为标签：

Wolfram Language code: PathGraph[Range[4], VertexLabels -> {1 -> [image], 2 -> [image], 3 -> [image]}, ImagePadding -> 20]

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[PathGraph[Range[4], VertexSize -> 0.1, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 4}], PlotLabel -> p], {p, {Before, After, Below, Above}}]

在角位置外的符号：

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

Wolfram Language code:

Table[PathGraph[Range[4], VertexSize -> 0.1, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 4}], PlotLabel -> p], {p, pl}]

在位置内的符号：

Wolfram Language code:

Table[PathGraph[Range[3], VertexSize -> 0.5, VertexLabels -> Table[i -> Placed["■■■", p], {i, 3}], VertexShapeFunction -> "Square", PlotLabel -> p], {p, {Left, Top, Right, Bottom}}]

角位置内的符号：

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

Wolfram Language code:

Table[PathGraph[Range[3], VertexSize -> 0.5, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 3}], PlotLabel -> p], {p, pl}]

使用显式坐标来放置标签的中心：

Wolfram Language code:

Table[PathGraph[Range[3], VertexSize -> 0.5, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed[[image], p], {i, 3}], PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

把所有标签放置在顶点的右上角，并且改变标签内的坐标：

Wolfram Language code:

Table[PathGraph[Range[3], VertexSize -> 0.5, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed[[image], {{1, 1}, p}], {i, 3}], PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

使用 Placed 在一个封装中放置多个标签：

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

可以使用任意数目的标签：

Wolfram Language code:

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

使用 VertexLabels 放置多个标签：

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

使用 Placed 的参数来控制包括 Tooltip 在内的格式：

Wolfram Language code: PathGraph[Range[4], VertexLabels -> Placed["Name", Tooltip]]

或者 StatusArea:

Wolfram Language code: PathGraph[Range[4], VertexLabels -> Placed["Name", StatusArea]]

使用更加精巧的格式化函数：

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

Wolfram Language code: PathGraph[Range[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: PathGraph[Range[4], VertexLabels -> Table[i -> Placed["xxx", Center, panelLabel], {i, 4}]]

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

Wolfram Language code: PathGraph[Range[4], VertexLabels -> Table[i -> Placed["xxx", Center, hyperlinkLabel], {i, 4}]]

VertexShape (5)

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

Wolfram Language code: Table[PathGraph[Range[4], VertexShape -> s, VertexSize -> Large], {s, {[image], [image], [image]}}]

指定单个顶点的顶点形状：

Wolfram Language code: PathGraph[Range[4], VertexShape -> {2 -> [image]}, VertexSize -> Large]

VertexShape 可以与 VertexSize 合起来使用：

Wolfram Language code: Table[PathGraph[Range[4], VertexSize -> s, VertexShape -> [image], PlotLabel -> s], {s, {Small, Large}}]

VertexShape 不受 VertexStyle 影响：

Wolfram Language code: PathGraph[Range[4], VertexSize -> 0.2, VertexShape -> [image], VertexStyle -> Blue]

VertexShapeFunction 具有比 VertexShape 更高的优先级：

Wolfram Language code: PathGraph[Range[4], VertexSize -> 0.1, VertexShapeFunction -> "Square", VertexShape -> [image]]

VertexShapeFunction (10)

获得 VertexShapeFunction 内置集合列表：

Wolfram Language code: ResourceData["VertexShapeFunction"]

使用 "Basic" 集合中 VertexShapeFunction 的内置设置：

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

简单的基本形状：

Wolfram Language code:

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

共同的基本形状：

Wolfram Language code:

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

使用 "Rounded" 集合中的 VertexShapeFunction 内置设定：

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

Wolfram Language code:

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

使用 "Concave" 集合中的 VertexShapeFunction 内置设定：

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

Wolfram Language code:

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

绘制单个顶点：

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

组合默认顶点函数：

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

使用预定义的图绘制顶点：

Wolfram Language code: PathGraph[Range[4], VertexShapeFunction -> (Inset[[image], #]&)]

通过运行程序绘制顶点：

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: PathGraph[Range[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: PathGraph[Range[4], VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf1]

VertexShapeFunction 比 VertexStyle 具有更高的优先级：

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

Wolfram Language code: PathGraph[Range[4], VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexShapeFunction 可以与 VertexSize 组合使用：

Wolfram Language code: PathGraph[Range[4], VertexShapeFunction -> "Star", VertexSize -> {2 -> 0.3, 0.2}]

VertexShapeFunction 比 VertexShape 具有更高的优先级：

Wolfram Language code: PathGraph[Range[4], VertexSize -> 0.3, VertexShapeFunction -> "Star", VertexShape -> [image]]

VertexSize (8)

默认情况下，自动计算顶点大小：

Wolfram Language code: PathGraph[Range[4], VertexSize -> Automatic]

使用符号顶点尺寸，指定所有顶点的大小：

Wolfram Language code: Table[PathGraph[Range[4], VertexSize -> s, PlotLabel -> s], {s, {Tiny, Small, Medium, Large}}]

使用顶点坐标之间最小距离的百分比：

Wolfram Language code: Table[PathGraph[Range[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比：

Wolfram Language code: Table[PathGraph[Range[4], VertexSize -> {"Scaled", s}, PlotLabel -> {"Scaled", s}], {s, 0.1, 1, 0.3}]

指定和方向上的大小：

Wolfram Language code: Table[PathGraph[Range[4], VertexSize -> s, PlotLabel -> s], {s, {{0.1, 0.2}, {0.2, 0.1}}}]

指定单个顶点大小：

Wolfram Language code: PathGraph[Range[4], VertexSize -> {1 -> 0.2, 2 -> 0.3}]

VertexSize 可以与 VertexShapeFunction 合起来使用：

Wolfram Language code: Table[PathGraph[Range[4], VertexSize -> s, VertexShapeFunction -> "Square", PlotLabel -> s], {s, {0.05, 0.1, 0.2}}]

VertexSize 可以与 VertexShape 合起来使用：

Wolfram Language code: Table[PathGraph[Range[4], VertexSize -> s, VertexShape -> [image], PlotLabel -> s], {s, {0.1, 0.2, 0.4}}]

VertexStyle (5)

对所有顶点进行样式化处理：

Wolfram Language code:

Table[PathGraph[Range[5], VertexStyle -> style, VertexSize -> 0.4, PlotLabel -> style], {style, {Yellow, EdgeForm[Dashed]}}]

对单个顶点进行样式化处理：

Wolfram Language code: PathGraph[Range[5], VertexStyle -> {1 -> Blue, 2 -> Red}, VertexSize -> 0.2]

VertexShapeFunction 可以与 VertexStyle 合起来使用：

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

Wolfram Language code: PathGraph[Range[5], 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: PathGraph[Range[5], VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexStyle 可以与 BaseStyle 联合：

Wolfram Language code: PathGraph[Range[5], VertexStyle -> LightBlue, BaseStyle -> EdgeForm[Dotted], VertexSize -> 0.4]

VertexStyle 具有比 BaseStyle 更高的优先级：

Wolfram Language code: PathGraph[Range[5], VertexStyle -> LightBlue, BaseStyle -> Gray, VertexSize -> 0.4]

VertexShape 不受 VertexStyle 影响：

Wolfram Language code: PathGraph[Range[5], VertexSize -> 0.4, VertexShape -> [image], VertexStyle -> Blue]

VertexWeight (2)

设置所有顶点的权：

Wolfram Language code: PathGraph[Range[4], VertexWeight -> {2, 3, 4, 5}]

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

使用任何数值表达式作为权：

Wolfram Language code: PathGraph[Range[4], VertexWeight -> {a, b, c, d}]

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

应用 (6)

路径图的 GraphCenter：

Wolfram Language code: Table[HighlightGraph[#, GraphCenter[#]]&[PathGraph[Range[i], VertexSize -> 0.2]], {i, 3, 6}]

GraphPeriphery：

Wolfram Language code: Table[HighlightGraph[#, GraphPeriphery[#]]&[PathGraph[Range[i], VertexSize -> 0.2]], {i, 3, 6}]

VertexEccentricity：

Wolfram Language code: VertexEccentricity[PathGraph[Range[20]], #]& /@ Range[4]

突出显示顶点偏心路径：

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 = PathGraph[Range[20], VertexSize -> Medium], FindVertexEccentricityPath[g, u]], {u, Range[4]}]

GraphRadius：

Wolfram Language code: Table[GraphRadius[PathGraph[Range[i]]], {i, 3, 6}]

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: Table[HighlightGraph[#, FindRadiusPath[#]]&[PathGraph[Range[i], VertexSize -> Medium]], {i, 3, 6}]

GraphDiameter：

Wolfram Language code: Table[GraphDiameter[PathGraph[Range[i]]], {i, 3, 6}]

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: Table[HighlightGraph[#, FindDiameterPath[#]]&[PathGraph[Range[i], VertexSize -> Medium]], {i, 3, 6}]

可视化 PathGraph 不同的中心性：

Wolfram Language code:

HighlightCentrality[g_, cc_] := HighlightGraph[g, Table[Style[VertexList[g][[i]], ColorData["TemperatureMap"][cc[[i]] / Max[cc]]], {i, VertexCount[g]}]];

Wolfram Language code: g = PathGraph[Range[25], VertexSize -> Large];

Wolfram Language code: HighlightCentrality[g, DegreeCentrality[g]]

突出显示紧密中心性：

Wolfram Language code: HighlightCentrality[g, ClosenessCentrality[g]]

突出显示特征向量中心性：

Wolfram Language code: HighlightCentrality[g, EigenvectorCentrality[g]]

属性和关系 (10)

使用 VertexCount 和 EdgeCount 来计算顶点数和边数：

Wolfram Language code: g = PathGraph[Range[20]]

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

使用 VertexList 和 EdgeList 以标准顺序列出顶点和边：

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

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

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

Wolfram Language code: {VertexList[g2], EdgeList[g2]}

邻接矩阵的行和列遵循 VertexList 给出的顺序：

Wolfram Language code: g = PathGraph[{ab, bc, c -> d}];

Wolfram Language code: VertexList[g]

Wolfram Language code: TableForm[Normal@AdjacencyMatrix[g], TableHeadings -> {s = Style[#, Blue]& /@ %, s}]

从一个图计算 IncidenceMatrix：

Wolfram Language code: g = PathGraph[{ab, bc, c -> d}];

Wolfram Language code: m = IncidenceMatrix[g];

行顺序由 VertexList 给出，列顺序由 EdgeList 给出：

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

Wolfram Language code: TableForm[Normal@m, TableHeadings -> {Style[#, Blue]& /@ VertexList[g], Style[#, Blue]& /@ EdgeList[g]}]

一个路径图是不带有回路的图：

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

Wolfram Language code: PathGraphQ[%]

以相同顶点起始和结束的路径图是一个圈图：

Wolfram Language code: CycleGraph[5]

Wolfram Language code: PathGraphQ[%]

一个路径图是连通的，并且每个顶点的最大度数为2：

Wolfram Language code: g = CycleGraph[5]

Wolfram Language code: {ConnectedGraphQ[g], PathGraphQ[g]}

Wolfram Language code: VertexDegree[g]

一个不具有重复顶点的路径图是一棵树：

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

没有重复顶点的路径图是无环的：

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

Wolfram Language code: AcyclicGraphQ[%]

一个路径图的线图与同构：

Wolfram Language code: PathGraph[Range[21]]

Wolfram Language code: {LineGraph[%], PathGraph[Range[20]]}

Wolfram Language code: IsomorphicGraphQ@@%

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

PathGraph

更多信息和选项

所有选项的列表

范例

基本范例 (2)

范围 (6)

连通性 (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 (6)

属性和关系 (10)

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