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MeanClusteringCoefficient[g]

gives the mean clustering coefficient of the graph g.

MeanClusteringCoefficient[{vw,…}]

uses rules vw to specify the graph g.

Details
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Examples  
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Scope  
Applications  
Properties & Relations  
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MeanClusteringCoefficient

MeanClusteringCoefficient[g]

gives the mean clustering coefficient of the graph g.

MeanClusteringCoefficient[{vw,…}]

uses rules vw to specify the graph g.

Details

  • MeanClusteringCoefficient is also known as the average or overall clustering coefficient.
  • The mean clustering coefficient of g is the mean over all local clustering coefficients of vertices of g.
  • MeanClusteringCoefficient works with undirected graphs, directed graphs, and multigraphs.

Examples

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Basic Examples  (2)

Find the mean clustering coefficient of a graph:

Wolfram Language code: MeanClusteringCoefficient[[image]]

Mean clustering coefficient in the Watts–Strogatz model as a function of rewiring probability:

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

Scope  (5)

MeanClusteringCoefficient works with undirected graphs:

Wolfram Language code: MeanClusteringCoefficient[[image]]

Directed graphs:

Wolfram Language code: MeanClusteringCoefficient[[image]]

Multigraphs:

Wolfram Language code: MeanClusteringCoefficient[[image]]

Use rules to specify the graph:

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

MeanClusteringCoefficient works with large graphs:

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

Applications  (2)

Mean clustering coefficient of a power grid network:

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

Compare to uniform random graphs:

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

Collaboration networks tend to have high mean clustering coefficients:

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

Compare to uniform random graphs:

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

Properties & Relations  (7)

MeanClusteringCoefficient is the mean over all local clustering coefficients of vertices:

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

The mean clustering coefficient is between 0 and 1:

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

For a graph with no vertices of degree greater than 1, the mean clustering coefficient is 0:

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

The mean clustering coefficient of a complete graph with at least three vertices is 1:

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

Distribution of mean clustering coefficient in BernoulliGraphDistribution:

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

Expected value:

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

Distribution of mean clustering coefficient in WattsStrogatzGraphDistribution:

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]]

With low rewiring probability and high mean vertex degree, the expected value is near :

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

With high rewiring probability, the expected value is near 0:

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

Distribution of mean clustering coefficient in BarabasiAlbertGraphDistribution:

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

Compare with GlobalClusteringCoefficient:

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

Text

Wolfram Research (2012), MeanClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html (updated 2015).

CMS

Wolfram Language. 2012. "MeanClusteringCoefficient." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html.

APA

Wolfram Language. (2012). MeanClusteringCoefficient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html

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: 13-June-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: 13-June-2026]}