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AdjacencyGraph[amat]

隣接行列 amat のグラフを与える．

AdjacencyGraph[{v1,v2,…},amat]

頂点 vi，隣接行列 amat のグラフを与える．

詳細とオプション
Details and Options Details and Options
予備知識
例題  
例  
スコープ  
オプション  
AnnotationRules  
DirectedEdges  
EdgeLabels  
Show More Show More
EdgeShapeFunction  
EdgeStyle  
EdgeWeight  
GraphHighlight  
GraphHighlightStyle  
GraphLayout  
PlotTheme  
基本テーマ  
特徴テーマ  
VertexCoordinates  
VertexLabels  
VertexShape  
VertexShapeFunction  
VertexSize  
VertexStyle  
VertexWeight  
アプリケーション  
特性と関係  
関連項目
関連するガイド
関連リンク
履歴
引用書式

AdjacencyGraph

AdjacencyGraph[amat]

隣接行列 amat のグラフを与える．

AdjacencyGraph[{v1,v2,…},amat]

頂点 vi，隣接行列 amat のグラフを与える．

詳細とオプション

予備知識

  • AdjacencyGraphは，無向グラフあるいは有向グラフの隣接行列表現からグラフを作る．隣接行列は，行と列がそれぞれグラフの頂点に当たり，要素 aijが頂点 viから頂点 vjまでの（有向）辺の数を表す非負の整数である正方行列である．対角項がある隣接行列は，自己ループを作る．
  • オプションDirectedEdges（可能な値はAutomatic．True，False）を使って有向グラフを作るか無向グラフを作るかを制御することができる．デフォルトで，AdjacencyGraphは，入力行列が対称行列の場合は無向グラフを，その他の場合は有向グラフを返す．
  • AdjacencyGraphはGraphと同じオプション（EdgeStyle，VertexStyle，EdgeLabels，VertexLabels，GraphLayout，VertexCoordinates等）を取る．AdjacencyGraphはグラフの重みは考慮しないので，重み付きの隣接行列からグラフを構築する場合はWeightedAdjacencyGraphを使わなければならない．
  • AdjacencyListは，指定された頂点 viに隣接する頂点のリスト，つまり隣接行列の i 番目の列（無向グラフの場合は i 番目の行）中の非零要素の位置のリストに相当するリストを返す．任意のグラフ（AdjacencyGraphによって構築されたグラフを含む）の隣接行列全体はAdjacencyMatrixで得ることができる．IncidenceGraphは，グラフの構築に，隣接行列の代りに指標行列表現を使う．

例題

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例  (2)

隣接行列からグラフを構築する：

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

対称隣接行列は結果として無向グラフになる：

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

スコープ  (7)

対称行列は無向グラフと解釈される：

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

非対称行列は有向グラフと解釈される：

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

DirectedEdgesを使って対称行列から有向グラフを構築する：

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

対角成分のある行列は自己ループを作る：

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 |)]}

SparseArrayオブジェクトを使って隣接行列を指定する：

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

デフォルトで，頂点は1から までの整数であるとみなされる：

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

明示的な頂点リストを使って頂点に名前を与える：

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は大きい行列にも使える：

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

オプション  (83)

AnnotationRules  (3)

頂点の注釈を指定する：

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

辺の注釈を指定する：

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

グラフ自体の注釈を指定する：

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

DirectedEdges  (3)

デフォルトで対称行列は無向グラフを生成する：

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を使って有向グラフを生成する：

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]]

デフォルトで非対称行列は有向グラフを生成する：

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)

辺12にラベルを付ける：

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

すべての辺に個別にラベルを付ける：

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]}]]

式をラベルとして使う：

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

Placedを記号位置と共に使って辺に沿ったラベルの置き方を制御する：

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"}}]

明示的な座標を使ってラベルを置く：

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}}]

ラベル内で位置を変える：

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}}}]

複数のラベルを置く：

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"}]}]

TooltipとStatusAreaの値を使って自動的にラベルを付ける：

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)

EdgeShapeFunctionの組込み設定のリストを得る：

Wolfram Language code: ResourceData["EdgeShapeFunction"]

基線を含む無向辺：

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

辺に異なるグリフがある線グラフ：

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"}}]

塗り潰された矢印を含む有向辺：

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"]}]

線による矢印：

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"]}]

塗り潰されていない矢印：

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"]}]

個別の辺に辺関数を指定する：

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

別のデフォルトの辺関数と組み合せる：

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

プログラムを実行して辺を描く：

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はEdgeStyleと組み合せることができる：

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

EdgeShapeFunctionはEdgeStyleより優先順位が高い：

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

EdgeStyle  (2)

すべての辺にスタイルを付ける：

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

個々の辺にスタイルを付ける：

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

EdgeWeight  (2)

すべての辺の重みを指定する：

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

任意の数式を重みとして使う：

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

GraphHighlight  (3)

頂点1をハイライトする：

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

辺23をハイライトする：

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

頂点と辺をハイライトする：

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

GraphHighlightStyle  (2)

GraphHighlightStyleの組込み設定のリストを得る：

Wolfram Language code: ResourceData["GraphHighlightStyle"]

GraphHighlightStyleの組込み設定を使う：

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)

デフォルトで，レイアウトは自動的に選ばれる：

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

特別な曲線上のレイアウトを指定する：

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

最適化の基準を満足するレイアウトを指定する：

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

VertexCoordinatesはGraphLayoutの座標を無効にする：

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}]]}

AbsoluteOptionsを使い，レイアウトアルゴリズムで計算されたVertexCoordinatesを抽出する：

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

PlotTheme  (4)

基本テーマ  (2)

一般的な基本テーマを使う：

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

白黒のテーマを使う：

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

特徴テーマ  (2)

大きいグラフのテーマを使う：

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

古典的な図表のテーマを使う：

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

VertexCoordinates  (3)

デフォルトで，任意の頂点座標が自動的に計算される：

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

AbsoluteOptionsを使って結果の頂点座標を抽出する：

Wolfram Language code: AbsoluteOptions[%, VertexCoordinates]

楕円に沿ったレイアウト関数を指定する：

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}]]]

上記を使ってグラフの頂点座標を生成する：

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

VertexCoordinatesはGraphLayoutより優先順位が高い：

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

VertexLabels  (13)

頂点名をラベルに使う：

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

個々の頂点にラベルを付ける：

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

すべての頂点にラベルを付ける：

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

任意の式をラベルとして使う：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexLabels -> {1 -> [image], 2 -> [image], 3 -> [image]}, ImagePadding -> 30]

Placedを記号位置と共に使って位置の外側を含むラベルの置き方を制御する：

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}}]

記号的な外側のコーナー位置：

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}]

記号的な内側の位置：

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}}]

記号的な内側のコーナー位置：

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}]

明示的な座標を使ってラベルの中心を置く：

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}}}]

すべてのラベルを頂点の右上のコーナーに置き，ラベル内の座標位置を変える：

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}}}]

複数のラベルを置く：

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

任意の数のラベルを使うことができる：

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

Placedの引数を使ってTooltipを含むフォーマットを制御する：

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

あるいはStatusAreaを含むフォーマットを制御する：

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

より高度なフォーマット関数を使う：

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)

任意のGraphics，Image，あるいはGraphics3Dを頂点の形として使う：

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

個別の頂点の形を指定する：

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

VertexShapeはVertexSizeと組み合せることができる：

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

VertexShapeはVertexStyleの影響を受けない：

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

VertexShapeFunctionはVertexShapeより優先順位が高い：

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

VertexShapeFunction  (10)

VertexShapeFunctionの組込みコレクションのリストを得る：

Wolfram Language code: ResourceData["VertexShapeFunction"]

"Basic"コレクションのVertexShapeFunctionの組込み設定を使う：

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

簡単な基本形：

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"}}]

一般的な基本形：

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"}}]

"Rounded"コレクションのVertexShapeFunctionの組込み設定を使う：

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"]}]

"Concave"コレクションのVertexShapeFunctionの組込み設定を使う：

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"]}]

個々の頂点を描く：

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

デフォルトの頂点関数と組み合せる：

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

定義済みのグラフィックスを使って頂点を描く：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexShapeFunction -> (Inset[[image], #]&)]

プログラムを実行して頂点を描く：

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はVertexStyleと組み合せることができる：

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はVertexStyleより優先順位が高い：

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はVertexSizeと組み合せることができる：

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

VertexShapeFunctionはVertexShapeより優先順位が高い：

Wolfram Language code: AdjacencyGraph[(| | | | | - | - | - | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |), VertexSize -> 0.3, VertexShapeFunction -> "Star", VertexShape -> [image]]

VertexSize  (8)

デフォルトで，頂点の大きさは自動的に計算される：

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

記号的な頂点サイズを使ってすべての頂点の大きさを指定する：

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

頂点座標間の最短距離との割合を使う：

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

すべての頂点座標の全体的な対角との割合を使う：

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}]

方向と 方向の両方で大きさを指定する：

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}}}]

個別の頂点の大きさを指定する：

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

VertexSizeはVertexShapeFunctionと組み合せることができる：

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はVertexShapeと組み合せることができる：

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)

すべての頂点にスタイルを付ける：

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]}}]

個々の頂点にスタイルを付ける：

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

VertexShapeFunctionはVertexStyleと組み合せることができる：

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はVertexStyleより優先順位が高い：

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はBaseStyleと組み合せることができる：

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

VertexStyleはBaseStyleより優先順位が高い：

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

VertexShapeはVertexStyleの影響を受けない：

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

VertexWeight  (2)

全頂点の重みを指定する：

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

任意の数式を重みとして使う：

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

アプリケーション  (2)

s〚i〛⊆s〚j〛であれば頂点 i がs〚i〛を表し辺 ij を持つ集合 s のリストからグラフを構築する：

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"]

s〚i〛がs〚j〛を分割する (s〚i〛∣s〚j〛)場合に ij となる整数 s のリストからグラフを構築する：

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"]

特性と関係  (6)

VertexCountとEdgeCountを使って頂点と辺を数える：

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]}

VertexListとEdgeListを使って標準的な順序で頂点と辺を列挙する：

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

グラフからAdjacencyMatrixを計算する：

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

グラフはその隣接行列から再構築することができる：

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

対角線上にある成分がすべて0である隣接行列は自己ループのないグラフを構築する：

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

対角上の1はすべて自己ループを示している：

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

対角の外側のすべての成分が1である隣接行列は完全グラフを構築する：

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言語関数， https://reference.wolfram.com/language/ref/AdjacencyGraph.html.

テキスト

Wolfram Research (2010), AdjacencyGraph, Wolfram言語関数， https://reference.wolfram.com/language/ref/AdjacencyGraph.html.

CMS

Wolfram Language. 2010. "AdjacencyGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AdjacencyGraph.html.

APA

Wolfram Language. (2010). AdjacencyGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AdjacencyGraph.html

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: 11-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: 11-August-2026]}