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ConnectedGraphQ[g]

如果图 g 是连通的，则给出 True；否则，给出 False.

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基本范例  
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按以下格式引用：

ConnectedGraphQ

ConnectedGraphQ[g]

如果图 g 是连通的，则给出 True；否则，给出 False.

更多信息

  • ConnectedGraphQ 适用于任意图对象.
  • 如果在每对顶点之间存在一条路径，则一个图是连通的.

范例

打开所有单元 关闭所有单元

基本范例  (2)

检验一个图是否是连通的：

Wolfram Language code: Graph[{12, 23, 31}]
Wolfram Language code: ConnectedGraphQ[%]

具有孤立顶点的图不是连通的：

Wolfram Language code: Graph[{1, 2, 3, 4}, {12, 23, 31}]
Wolfram Language code: ConnectedGraphQ[%]

范围  (6)

检验无向图：

Wolfram Language code: ConnectedGraphQ[[image]]

有向图：

Wolfram Language code: ConnectedGraphQ[[image]]

多重图：

Wolfram Language code: ConnectedGraphQ[[image]]

混合图：

Wolfram Language code: ConnectedGraphQ[[image]]

对于任何非连通图，ConnectedGraphQ 给出 False：

Wolfram Language code: ConnectedGraphQ[x]

ConnectedGraphQ 可用于大规模图：

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: Timing[ConnectedGraphQ[g]]

应用  (1)

计算 Watts–Strogatz 随机图模型连通的概率：

Wolfram Language code: 𝒢 = WattsStrogatzGraphDistribution[20, 0.5, 1];
Wolfram Language code: 𝒟 = GraphPropertyDistribution[Boole[ConnectedGraphQ[g]], g𝒢];
Wolfram Language code: NProbability[x == 1, x𝒟]

属性和关系  (5)

一个连通图的距离矩阵不具有 元素：

Wolfram Language code: g = CycleGraph[3]

连通图：

Wolfram Language code: GraphDistanceMatrix[g]//MatrixForm

非连通图：

Wolfram Language code: g = Graph[{12, 34}]
Wolfram Language code: GraphDistanceMatrix[g]//MatrixForm

具有 个顶点的连通图的最小边数为 ：

Wolfram Language code: PetersenGraph[5, 2]
Wolfram Language code: {ConnectedGraphQ[%], EdgeCount[%] ≥ VertexCount[%] - 1}

具有 个顶点的路径图恰好有 条边：

Wolfram Language code: PathGraph[Range[10]]
Wolfram Language code: {ConnectedGraphQ[%], EdgeCount[%] ≥ VertexCount[%] - 1}

对于简单图，连通图的顶点度之和大于 ：

Wolfram Language code: g = WheelGraph[4]
Wolfram Language code: {ConnectedGraphQ[g], Total[VertexDegree[g]] ≥ (VertexCount[g] - 1) / 2}

一个非连通图：

Wolfram Language code: g = Graph[Range[10], {12}]
Wolfram Language code: {ConnectedGraphQ[g], Total[VertexDegree[g]] ≥ (VertexCount[g] - 1) / 2}

一个无向树是连通的：

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

一个无向路径是连通的：

Wolfram Language code: PathGraph[Range[10]]
Wolfram Language code: {PathGraphQ[%], ConnectedGraphQ[%]}
Wolfram Research (2010)，ConnectedGraphQ，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ConnectedGraphQ.html.

文本

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_connectedgraphq, author="Wolfram Research", title="{ConnectedGraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ConnectedGraphQ.html}", note=[Accessed: 15-October-2026]}

BibLaTeX

@online{reference.wolfram_2026_connectedgraphq, organization={Wolfram Research}, title={ConnectedGraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/ConnectedGraphQ.html}, note=[Accessed: 15-October-2026]}