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MeanClusteringCoefficient[g]

给出图 g 的平均聚类系数.

MeanClusteringCoefficient[{vw,…}]

使用 vw 规则指定图 g.

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MeanClusteringCoefficient

MeanClusteringCoefficient[g]

给出图 g 的平均聚类系数.

MeanClusteringCoefficient[{vw,…}]

使用 vw 规则指定图 g.

更多信息

范例

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基本范例  (2)

求一个图的平均聚类系数：

Wolfram Language code: MeanClusteringCoefficient[[image]]

Watts–Strogatz 模型中的平均聚类系数是一个重连概率的函数：

Wolfram Language code: Plot[MeanClusteringCoefficient[RandomGraph[WattsStrogatzGraphDistribution[10 ^ 3, p, 5]]], {p, 0, 1}, MaxRecursion -> 0]

范围  (5)

MeanClusteringCoefficient 适用于无向图：

Wolfram Language code: MeanClusteringCoefficient[[image]]

有向图：

Wolfram Language code: MeanClusteringCoefficient[[image]]

多图：

Wolfram Language code: MeanClusteringCoefficient[[image]]

使用规则来指定图：

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

MeanClusteringCoefficient 适用于大图：

Wolfram Language code: g = CirculantGraph[10000, Range[20]];
Wolfram Language code: MeanClusteringCoefficient[g]//Timing

应用  (2)

电网网格的平均聚类系数：

Wolfram Language code: g = ExampleData[{"NetworkGraph", "PowerGrid"}];
Wolfram Language code: N[MeanClusteringCoefficient[g]]

比较均匀随机图：

Wolfram Language code: 𝒟 = GraphPropertyDistribution[MeanClusteringCoefficient[h], hUniformGraphDistribution[VertexCount[g], EdgeCount[g]]];
Wolfram Language code: N[Mean[RandomVariate[𝒟, 1000]]]

协作网络往往有较高的平均聚类系数：

Wolfram Language code: g = ExampleData[{"NetworkGraph", "HighEnergyTheoryCollaborations"}];
Wolfram Language code: N[MeanClusteringCoefficient[g]]

比较均匀随机图：

Wolfram Language code: 𝒟 = GraphPropertyDistribution[MeanClusteringCoefficient[h], hUniformGraphDistribution[VertexCount[g], EdgeCount[g]]];
Wolfram Language code: N[Mean[RandomVariate[𝒟, 1000]]]

属性和关系  (7)

MeanClusteringCoefficient 是顶点所有局部聚类系数的平均：

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

平均聚类系数介于 0 和 1 之间：

Wolfram Language code: RandomGraph[UniformGraphDistribution[20, 50]]
Wolfram Language code: N[MeanClusteringCoefficient[%]]

对于没有顶点度大于1的图，平均聚类系数为0：

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

具有至少3个顶点的完全图的平均聚类系数为1：

Wolfram Language code: CompleteGraph[5]
Wolfram Language code: MeanClusteringCoefficient[%]

BernoulliGraphDistribution 中平均聚类系数的分布：

Wolfram Language code: 𝒟 = GraphPropertyDistribution[MeanClusteringCoefficient[g], gBernoulliGraphDistribution[8, 0.6]];
Wolfram Language code: Histogram[RandomVariate[𝒟, 1000]]

期望值：

Wolfram Language code: NExpectation[x, x𝒟]

WattsStrogatzGraphDistribution 中平均聚类系数的分布：

Wolfram Language code: 𝒟[n_, p_, k_] := GraphPropertyDistribution[MeanClusteringCoefficient[g], gWattsStrogatzGraphDistribution[n, p, k]];
Wolfram Language code: Histogram[RandomVariate[𝒟[50, 0.05, 3], 1000]]

低重连概率和高平均顶点度的期望值接近于 ：

Wolfram Language code: NExpectation[x, x𝒟[100, 0.01, 20]]

高重连概率的期望值接近0：

Wolfram Language code: NExpectation[x, x𝒟[100, 0.99, 2]]

BarabasiAlbertGraphDistribution 中平均聚类系数的分布：

Wolfram Language code: 𝒢 = BarabasiAlbertGraphDistribution[100, 10];
Wolfram Language code: data = RandomVariate[GraphPropertyDistribution[MeanClusteringCoefficient[g], g𝒢], 1000];
Wolfram Language code: Histogram[data]

与 GlobalClusteringCoefficient 相比较：

Wolfram Language code: data2 = RandomVariate[GraphPropertyDistribution[GlobalClusteringCoefficient[g], g𝒢], 1000];
Wolfram Language code: Histogram[{data, data2}]
Wolfram Research (2012)，MeanClusteringCoefficient，Wolfram 语言函数，https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html （更新于 2015 年）.

文本

Wolfram Research (2012)，MeanClusteringCoefficient，Wolfram 语言函数，https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html （更新于 2015 年）.

CMS

Wolfram 语言. 2012. "MeanClusteringCoefficient." 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/MeanClusteringCoefficient.html.

APA

Wolfram 语言. (2012). MeanClusteringCoefficient. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html 年

BibTeX

@misc{reference.wolfram_2026_meanclusteringcoefficient, author="Wolfram Research", title="{MeanClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}", note=[Accessed: 06-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_meanclusteringcoefficient, organization={Wolfram Research}, title={MeanClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}, note=[Accessed: 06-November-2026]}