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TopologicalSort[g]

给出有向无环图 g 中 g 的顶点按拓扑排序所得的列表.

TopologicalSort[{vw,…}]

用 vw 指定图 g.

更多信息
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范例  
基本范例  
范围  
应用  
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TopologicalSort

TopologicalSort[g]

给出有向无环图 g 中 g 的顶点按拓扑排序所得的列表.

TopologicalSort[{vw,…}]

用 vw 指定图 g.

更多信息

  • TopologicalSort 亦称为 topological ranking 或 topological ordering.
  • 如果对于每条边 uv，u 都先于 v，则顶点列表是按拓扑排序的.

范例

打开所有单元 关闭所有单元

基本范例  (1)

求顶点的拓扑顺序：

Wolfram Language code: g = [image];
Wolfram Language code: TopologicalSort[g]

范围  (6)

TopologicalSort 适用于有向图：

Wolfram Language code: TopologicalSort[[image]]

加权图：

Wolfram Language code: TopologicalSort[[image]]

多重图：

Wolfram Language code: TopologicalSort[[image]]

TopologicalSort 只适用于无环图：

Wolfram Language code: TopologicalSort /@ {[image], [image]}

用规则指定图：

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

适用于大型图：

Wolfram Language code: adj = SparseArray[{i_, j_} /; j > i :> If[RandomReal[] < 0.05, 1, 0], {10^3, 10^3}]; ind = RandomSample[Range[Length[adj]], Length[adj]]; g = AdjacencyGraph[adj[[ind, ind]]];
Wolfram Language code: Timing[TopologicalSort[g]//Length]
Wolfram Language code: {VertexCount[g], EdgeCount[g]}

应用  (1)

当有循环时，排序强连通分量而不是顶点：

Wolfram Language code: g = [image];
Wolfram Language code: components = ConnectedComponents[g]

通过找到分量间的边，构建 g 的凝结：

Wolfram Language code: edges = Union[Cases[EdgeList[g] /. Table[v -> First[Select[components, MemberQ[#, v]&]], {v, VertexList[g]}], u_v_ /; u =!= v]];
Wolfram Language code: cond = Graph[components, edges]

使用强连通分量的拓扑排序来排序 g 的顶点：

Wolfram Language code: TopologicalSort[cond]
Wolfram Language code: h = Graph[Join@@%, EdgeList[g], Options[g]]

新的邻接矩阵是上三角块：

Wolfram Language code: ArrayPlot /@ {AdjacencyMatrix[g], AdjacencyMatrix[h]}
Wolfram Research (2010)，TopologicalSort，Wolfram 语言函数，https://reference.wolfram.com/language/ref/TopologicalSort.html （更新于 2015 年）.

文本

Wolfram Research (2010)，TopologicalSort，Wolfram 语言函数，https://reference.wolfram.com/language/ref/TopologicalSort.html （更新于 2015 年）.

CMS

Wolfram 语言. 2010. "TopologicalSort." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2015. https://reference.wolfram.com/language/ref/TopologicalSort.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_topologicalsort, author="Wolfram Research", title="{TopologicalSort}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/TopologicalSort.html}", note=[Accessed: 31-October-2026]}

BibLaTeX

@online{reference.wolfram_2026_topologicalsort, organization={Wolfram Research}, title={TopologicalSort}, year={2015}, url={https://reference.wolfram.com/language/ref/TopologicalSort.html}, note=[Accessed: 31-October-2026]}