WOLFRAM

Wolfram 语言与系统参考资料中心

AdjacencyGraph[amat]

给出邻接矩阵为 amat 的图.

AdjacencyGraph[{v1,v2,…},amat]

给出顶点为 vi、邻接矩阵为 amat 的图.

更多信息和选项
Details and Options Details and Options
背景
范例  
基本范例  
范围  
选项  
AnnotationRules  
DirectedEdges  
EdgeLabels  
Show More Show More
EdgeShapeFunction  
EdgeStyle  
EdgeWeight  
GraphHighlight  
GraphHighlightStyle  
GraphLayout  
PlotTheme  
Base Themes  
Feature Themes  
VertexCoordinates  
VertexLabels  
VertexShape  
VertexShapeFunction  
VertexSize  
VertexStyle  
VertexWeight  
应用  
属性和关系  
参见
相关指南
相关链接
历史
按以下格式引用：

AdjacencyGraph

AdjacencyGraph[amat]

给出邻接矩阵为 amat 的图.

AdjacencyGraph[{v1,v2,…},amat]

给出顶点为 vi、邻接矩阵为 amat 的图.

更多信息和选项

背景

范例

打开所有单元 关闭所有单元

基本范例  (2)

从邻接矩阵构建一个图：

Wolfram Language code: AdjacencyGraph[{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}}]

对称邻接矩阵产生无向图：

Wolfram Language code: AdjacencyGraph[{{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}]

范围  (7)

对称矩阵被解释为无向图：

Wolfram Language code: AdjacencyGraph[(| | | | | | - | - | - | - | | 0 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 |)]

非对称矩阵被解释为有向图：

Wolfram Language code: AdjacencyGraph[(| | | | | | - | - | - | - | | 0 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 0 | 0 |)]

利用 DirectedEdges 从对称矩阵创建有向图：

Wolfram Language code: AdjacencyGraph[(| | | | | | - | - | - | - | | 0 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 |), DirectedEdges -> True]

具有对角线元素的矩阵将产生自环：

Wolfram Language code: {AdjacencyGraph[(| | | | | | - | - | - | - | | 1 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 |)], AdjacencyGraph[(| | | | | | - | - | - | - | | 0 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | | 1 | 1 | 1 | 0 | | 1 | 1 | 0 | 0 |)]}

利用一个 SparseArray 对象指定邻接矩阵：

Wolfram Language code: AdjacencyGraph[SparseArray[{{i_, j_} /; 0 < Abs[i - j] ≤ 3 -> 1}, {6, 6}]]

默认情况下，顶点采用从 1 到 的整数值：

Wolfram Language code: VertexList@AdjacencyGraph[(| | | | | | - | - | - | - | | 1 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 |)]

使用一个显式的顶点列表来给出顶点名称：

Wolfram Language code: VertexList@AdjacencyGraph[{a, b, c, d}, (| | | | | | - | - | - | - | | 1 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 |)]

AdjacencyGraph 可用于大规模矩阵：

Wolfram Language code: SparseArray[{Band[{2, 1}] -> 1, Band[{3, 1}] -> 1}, {10^6, 10^6}]
Wolfram Language code: Timing[AdjacencyGraph[%]//EdgeCount]

选项  (83)

AnnotationRules  (3)

指定顶点的注释:

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), AnnotationRules -> {3 -> {VertexLabels -> "hello"}}]

边：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), AnnotationRules -> {12 -> {EdgeLabels -> "hello"}}]

图自身：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), AnnotationRules -> {"GraphProperties" -> {"Message" -> "hello"}}]
Wolfram Language code: AnnotationValue[%, "Message"]

DirectedEdges  (3)

默认情况下，一个对称矩阵生成一个无向图：

Wolfram Language code: AdjacencyGraph[(| | | | | | | - | - | - | - | - | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 |)]

使用 DirectedEdges->True 来生成一个有向图：

Wolfram Language code: AdjacencyGraph[(| | | | | | | - | - | - | - | - | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 |), DirectedEdges -> True, EdgeStyle -> Arrowheads[Medium]]

默认情况下，一个非对称矩阵生成一个有向图：

Wolfram Language code: AdjacencyGraph[(| | | | | | | - | - | - | - | - | | 0 | 1 | 1 | 1 | 1 | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 |)]

EdgeLabels  (7)

对边 12 添加标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> {12 -> "Hello"}]

对每个边分别添加标签：

Wolfram Language code: el = {12, 13, 23};
Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> Table[el[[i]] -> Subscript["e", i], {i, Length[el]}]]

使用任意表达式作为标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> {12 -> [image], 23 -> [image], 13 -> [image]}]

使用符号位置信息的 Placed 来控制沿着一条边的标签位置：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> {12 -> Placed["■■■", p]}, PlotLabel -> p, BaselinePosition -> Bottom], {p, {0, 1 / 4, 1 / 3}}]

改变标签内的位置：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> {12 -> Placed["■■■", {1 / 2, p}]}, PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

放置多个标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> {31 -> Placed[{"lbl1", "lbl2"}, {"Start", "End"}]}]
Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> {31 -> Placed[{"lbl1", "lbl2", "lbl3"}, {"Start", "Middle", "End"}]}]

通过 Tooltip 和 StatusArea 的值，使用自动标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> Placed["Name", Tooltip]]
Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeLabels -> Placed["Name", StatusArea]]

EdgeShapeFunction  (6)

获取 EdgeShapeFunction 的内置设置列表：

Wolfram Language code: ResourceData["EdgeShapeFunction"]

包含基本线条的无向边：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeShapeFunction -> "Line"]

具有各种符号的边线条：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |), EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "FilledArrow"]}]

线型箭头：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |), EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "UnfilledArrow"]}]

开放式箭头：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |), EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "CarvedArrow"]}]

对每条边指定一个边函数：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |), EdgeShapeFunction -> {12 -> "FilledArcArrow"}]

与一个不同的默认边函数合用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeShapeFunction -> ef]

EdgeShapeFunction 可以与 EdgeStyle 合起来使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeStyle -> Blue, EdgeShapeFunction -> (Line[#1]&)]

EdgeShapeFunction 具有比 EdgeStyle 更高的优先级：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeStyle -> Blue, EdgeShapeFunction -> ({Red, Line[#1]}&)]

EdgeStyle  (2)

对所有边进行样式化处理：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeStyle -> style, PlotLabel -> style], {style, {Gray, Dashed, Thick}}]

对单条边进行样式化处理：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeStyle -> {12 -> Blue, 13 -> Dashed}]

EdgeWeight  (2)

指定所有边的权值：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeWeight -> RandomInteger[5, 3]]
Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

将任意数值表达式作为权值使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), EdgeWeight -> {a, b, c}]
Wolfram Language code: WeightedAdjacencyMatrix[%]//MatrixForm

GraphHighlight  (3)

突出显示顶点 1：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> Tiny, GraphHighlight -> {1}]

突出显示边 23：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> Tiny, GraphHighlight -> {23}]

突出显示顶点和边：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> Tiny, GraphHighlight -> {1, 2, 2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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), GraphLayout -> Automatic]

指定在特殊曲线上的布局：

Wolfram Language code: m = AdjacencyMatrix[GridGraph[{10, 10}]];
Wolfram Language code: Table[AdjacencyGraph[m, GraphLayout -> l, PlotLabel -> l], {l, {"CircularEmbedding", "SpiralEmbedding"}}]

指定满足最优化标准的布局：

Wolfram Language code: m = AdjacencyMatrix[GridGraph[{10, 10}]];
Wolfram Language code: Table[AdjacencyGraph[m, GraphLayout -> l, PlotLabel -> l], {l, {"SpringEmbedding", "SpringElectricalEmbedding", "HighDimensionalEmbedding"}}]

VertexCoordinates 重载 GraphLayout 坐标：

Wolfram Language code: {AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), GraphLayout -> "SpringElectricalEmbedding"], AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), GraphLayout -> "SpringElectricalEmbedding", VertexCoordinates -> Table[{i, i}, {i, 0, 2}]]}

通过一个布局算法，利用 AbsoluteOptions 提取计算所得的 VertexCoordinates：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |)]
Wolfram Language code: AbsoluteOptions[%, VertexCoordinates]

PlotTheme  (4)

Base Themes  (2)

使用公共基础主题：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), PlotTheme -> "Business"]

使用一个单色的主题：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), PlotTheme -> "Monochrome"]

Feature Themes  (2)

使用大型图主题：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), PlotTheme -> "LargeGraph"]

使用经典图表主题：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), PlotTheme -> "ClassicDiagram"]

VertexCoordinates  (3)

默认情况下，自动计算任意顶点坐标：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |)]

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}]]]

使用它来生成顶点坐标：

Wolfram Language code: m = AdjacencyMatrix[PathGraph[Range[20]]];
Wolfram Language code: AdjacencyGraph[m, VertexCoordinates -> ellipseLayout[20, {2, 1}]]

VertexCoordinates 具有比 GraphLayout 更高的优先级：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexCoordinates -> Table[{i, i}, {i, 3}], GraphLayout -> "CircularEmbedding"]

VertexLabels  (13)

将顶点名称作为标签使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> "Name"]

对单个顶点添加标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> {1 -> "one"}]

对所有顶点添加标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> Table[i -> Subscript[v, i], {i, 3}]]

将任意表达式作为标签使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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，包括内部位置：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.1, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 3}], PlotLabel -> p, ImagePadding -> 20], {p, {Before, After, Below, Above}}]

拐角位置外的符号表示：

Wolfram Language code: pl = {{Before, Below}, {After, Below}, {Before, Above}, {After, Above}};
Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.1, VertexShapeFunction -> "Square", ImagePadding -> 20, VertexLabels -> Table[i -> Placed["■■■", p], {i, 3}], PlotLabel -> p], {p, pl}]

内部位置的符号表示：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.25, VertexLabels -> Table[i -> Placed["■■■", p], {i, 3}], VertexShapeFunction -> "Square", PlotLabel -> p], {p, {Left, Top, Right, Bottom}}]

内拐角位置的符号表示：

Wolfram Language code: pl = {{Left, Bottom}, {Right, Bottom}, {Left, Top}, {Right, Top}};
Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.25, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed["■■■", p], {i, 3}], PlotLabel -> p], {p, pl}]

使用显式坐标来放置标签中心：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.25, VertexShapeFunction -> "Square", VertexLabels -> Table[i -> Placed[[image], p], {i, 3}], PlotLabel -> p, BaselinePosition -> Bottom], {p, {{0, 0}, {1 / 2, 1 / 2}, {1, 1}}}]

把所有标签放在顶点的右上角，并且在标签内改变坐标：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.35, 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}}}]

放置多个标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> {3 -> Placed[{"lbl1", "lbl2"}, {Above, Below}]}]

可以使用任意数目的标签：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> {3 -> Placed[{"lbl1", "lbl2", "lbl3", "lbl4"}, {Above, After, Below, Before}]}]

使用参数 Placed 来控制格式，包括 Tooltip：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> Placed["Name", Tooltip]]

或者 StatusArea:

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> Placed["Name", StatusArea]]

使用更美观的格式函数：

Wolfram Language code: rotateLabel[lab_] := Rotate[lab, 45Degree]
Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> Table[i -> Placed["xxx", Below, rotateLabel], {i, 3}]]
Wolfram Language code: panelLabel[lab_] := Panel[lab, FrameMargins -> 0, Background -> Lighter[Blue, 0.7]]
Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> Table[i -> Placed["xxx", Center, panelLabel], {i, 3}]]
Wolfram Language code: hyperlinkLabel[lab_] := Hyperlink[lab, "http://www.wolfram.com"]
Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> Table[i -> Placed["xxx", Center, hyperlinkLabel], {i, 3}]]

VertexShape  (5)

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

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShape -> s, VertexSize -> Medium], {s, {[image], [image], [image]}}]

对单个顶点，指定顶点形状：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShape -> {2 -> [image]}, VertexSize -> Small]

VertexShape 可以与 VertexSize 合起来使用：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> s, VertexShape -> [image], PlotLabel -> s], {s, {Small, Large}}]

VertexShape 不受 VertexStyle 影响：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.2, VertexShape -> [image], VertexStyle -> Blue]

VertexShapeFunction 具有比 VertexShape 更高的优先级：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.2, VertexShapeFunction -> "Square", VertexShape -> [image]]

VertexShapeFunction  (10)

获取 VertexShapeFunction 的内置设置列表：

Wolfram Language code: ResourceData["VertexShapeFunction"]

利用 VertexShapeFunction 在 "Basic" 集合中的内置设置：

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

简单基本形状：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, {"Triangle", "Square", "Rectangle", "Pentagon", "Hexagon", "Octagon"}}]

普通基本形状：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, {"DownTrapezoid", "UpTrapezoid", "Parallelogram", "FiveDown", "Circle", "Diamond", "Star", "Capsule"}}]

使用 VertexShapeFunction 在 "Rounded" 集合中的内置设置：

Wolfram Language code: ResourceData["VertexShapeFunction", "Rounded"]
Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, ResourceData["VertexShapeFunction", "Rounded"]}]

使用 VertexShapeFunction 在 "Concave" 集合中的内置设置：

Wolfram Language code: ResourceData["VertexShapeFunction", "Concave"]
Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, ResourceData["VertexShapeFunction", "Concave"]}]

绘制单个顶点：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> { 1 -> "Square"}, VertexSize -> 0.2]

与默认的顶点函数合起来使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> { 1 -> "Square", "Triangle"}, VertexSize -> 0.2]

使用预定义的图形绘制顶点：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> vf, 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexShapeFunction 可以与 VertexSize 合起来使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> "Star", VertexSize -> {1 -> Small, Medium}]

VertexShapeFunction 具有比 VertexShape 更高的优先级：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> Automatic]

使用符号顶点尺寸，指定所有顶点的大小：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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比：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> s, PlotLabel -> s], {s, 0.1, 1, 0.3}]

对所有顶点坐标，使用整体对角线比率：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> {"Scaled", s}, PlotLabel -> {"Scaled", s}], {s, 0.1, 1, 0.3}]

指定在 和 方向上的尺寸：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> s, PlotLabel -> s], {s, {{0.1, 0.2}, {0.2, 0.1}}}]

对单个顶点，指定大小：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> {1 -> 0.2, 2 -> 0.3}]

VertexSize 可以与 VertexShapeFunction 合起来使用：

Wolfram Language code: Table[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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[AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexStyle -> style, VertexSize -> 0.3, PlotLabel -> style], {style, {Yellow, EdgeForm[Dashed]}}]

对单个顶点进行样式化处理：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), 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: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexStyle 可以与 BaseStyle 合起来使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexStyle -> LightBlue, BaseStyle -> EdgeForm[Dotted], VertexSize -> 0.2]

VertexStyle 具有比 BaseStyle 更高的优先级：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexStyle -> LightBlue, BaseStyle -> Gray, VertexSize -> 0.2]

VertexShape 不受 VertexStyle 影响：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.2, VertexShape -> [image], VertexStyle -> Blue]

VertexWeight  (2)

设置所有顶点的权值：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexWeight -> {2, 3, 4}]
Wolfram Language code: AnnotationValue[{%, 1}, VertexWeight]

将任意数值表达式作为权值使用：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexWeight -> {a, b, c}]
Wolfram Language code: AnnotationValue[{%, 1}, VertexWeight]

应用  (2)

从集合列表 s 构建一个图，其中顶点 i 表示 s〚i〛 并且具有一条边 ij 如果 s〚i〛⊆s〚j〛:

Wolfram Language code: s = Subsets[{1, 2, 3}]
Wolfram Language code: AdjacencyGraph[s, Table[Boole@SubsetQ[s[[i]], s[[j]]], {i, Length[s]}, {j, Length[s]}], VertexLabels -> "Name"]

从整数列表 s 构建一个图，其中 ij 如果 s〚i〛 整除 s〚j〛 (s〚i〛∣s〚j〛):

Wolfram Language code: s = Divisors[24]
Wolfram Language code: AdjacencyGraph[s, Table[Boole@Divisible[s[[i]], s[[j]]], {i, Length[s]}, {j, Length[s]}], VertexLabels -> "Name"]

属性和关系  (6)

使用 VertexCount 和 EdgeCount 计算顶点数和边数：

Wolfram Language code: g = AdjacencyGraph[(| | | | | | | - | - | - | - | - | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 |)]
Wolfram Language code: {VertexCount[g], EdgeCount[g]}

利用 VertexList 和 EdgeList 以标准顺序列出顶点和边：

Wolfram Language code: g = AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |)]
Wolfram Language code: {VertexList[g], EdgeList[g]}

计算一个图的 AdjacencyMatrix：

Wolfram Language code: g = AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 0 | | 0 | 0 | 1 | | 1 | 0 | 0 |)];
Wolfram Language code: AdjacencyMatrix[g]//MatrixForm

一个图可以通过邻接矩阵重建：

Wolfram Language code: CompleteGraph[5]
Wolfram Language code: AdjacencyGraph [AdjacencyMatrix[%]]

对角线元素全是零的邻接矩阵生成的是一个没有自环的图：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |)]
Wolfram Language code: LoopFreeGraphQ[%]

对角线上的每个1表示一个自环：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 1 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 |)]

如果对于一个邻接矩阵，所有对角线外的元素都是1的话，该邻接矩阵所对应的图是一个完全图：

Wolfram Language code: m = (| | | | | | | - | - | - | - | - | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 |);
Wolfram Language code: MatrixPlot[m]
Wolfram Language code: AdjacencyGraph[m]
Wolfram Language code: CompleteGraphQ[%]
Wolfram Research (2010)，AdjacencyGraph，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AdjacencyGraph.html.

文本

Wolfram Research (2010)，AdjacencyGraph，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AdjacencyGraph.html.

CMS

Wolfram 语言. 2010. "AdjacencyGraph." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/AdjacencyGraph.html.

APA

Wolfram 语言. (2010). AdjacencyGraph. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/AdjacencyGraph.html 年

BibTeX

@misc{reference.wolfram_2026_adjacencygraph, author="Wolfram Research", title="{AdjacencyGraph}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/AdjacencyGraph.html}", note=[Accessed: 18-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_adjacencygraph, organization={Wolfram Research}, title={AdjacencyGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/AdjacencyGraph.html}, note=[Accessed: 18-August-2026]}