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LocalClusteringCoefficient[g]

gives the list of local clustering coefficients of all vertices in the graph g.

LocalClusteringCoefficient[g,v]

gives the local clustering coefficient of the vertex v in the graph g.

LocalClusteringCoefficient[{vw,…},…]

uses rules vw to specify the graph g.

Details
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LocalClusteringCoefficient

LocalClusteringCoefficient[g]

gives the list of local clustering coefficients of all vertices in the graph g.

LocalClusteringCoefficient[g,v]

gives the local clustering coefficient of the vertex v in the graph g.

LocalClusteringCoefficient[{vw,…},…]

uses rules vw to specify the graph g.

Details

  • LocalClusteringCoefficient is also known as clustering coefficient.
  • The local clustering coefficient of the vertex v is the fraction of pairs of neighbors of v that are connected over all pairs of neighbors of v.
  • LocalClusteringCoefficient works with undirected graphs, directed graphs, and multigraphs.

Examples

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Basic Examples  (2)

Compute local clustering coefficients:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Friendship"}];
Wolfram Language code: LocalClusteringCoefficient[g]

Highlight:

Wolfram Language code: HighlightGraph[g, VertexSize -> Thread[VertexList[g] -> %]]

Distribution of local clustering coefficients in a graph:

Wolfram Language code: g = RandomGraph[BarabasiAlbertGraphDistribution[10000, 50]];
Wolfram Language code: Histogram[LocalClusteringCoefficient[g]]

Scope  (6)

LocalClusteringCoefficient works with undirected graphs:

Wolfram Language code: LocalClusteringCoefficient[[image]]

Directed graphs:

Wolfram Language code: LocalClusteringCoefficient[[image]]

Multigraphs:

Wolfram Language code: LocalClusteringCoefficient[[image]]

Find the local clustering coefficient of a vertex:

Wolfram Language code: LocalClusteringCoefficient[[image], 1]

Use rules to specify the graph:

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

LocalClusteringCoefficient works with large graphs:

Wolfram Language code: g = RandomGraph[WattsStrogatzGraphDistribution[10000, 0.05, 20]];
Wolfram Language code: LocalClusteringCoefficient[g]//Short//Timing

Applications  (2)

Local clustering coefficients of the internet at the level of autonomous systems:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Internet"}];
Wolfram Language code: c = LocalClusteringCoefficient[g]; Histogram[c]

Plot the mean as a function of the vertex degree:

Wolfram Language code: d = Union[VertexDegree[g]];
Wolfram Language code: ListLogLogPlot[Table[{i, Mean[Pick[c, VertexDegree[g], i]]}, {i, d}]]

Local clustering coefficients of Zachary's Karate Club:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "ZacharyKarateClub"}]
Wolfram Language code: c = LocalClusteringCoefficient[g]

Highlight vertices based on their local clustering coefficients:

Wolfram Language code: HighlightGraph[g, Table[Style[VertexList[g][[i]], ColorData["TemperatureMap"][c[[i]]]], {i, VertexCount[g]}]]

Properties & Relations  (4)

The local clustering coefficients take values between 0 and 1:

Wolfram Language code: g = RandomGraph[BarabasiAlbertGraphDistribution[50, 3]]
Wolfram Language code: {Min[LocalClusteringCoefficient[g]], Max[LocalClusteringCoefficient[g]]}

The local clustering coefficient of a vertex with less than two neighbors is 0:

Wolfram Language code: Graph[{12, 23}, VertexShapeFunction -> "Name"]
Wolfram Language code: LocalClusteringCoefficient[%, 3]

All local clustering coefficients of a complete graph with at least three vertices are 1:

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

MeanClusteringCoefficient gives the mean of LocalClusteringCoefficient:

Wolfram Language code: Graph[{12, 13, 23, 24, 34}]
Wolfram Language code: {MeanClusteringCoefficient[%], Mean[LocalClusteringCoefficient[%]]}
Wolfram Research (2012), LocalClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html (updated 2015).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_localclusteringcoefficient, author="Wolfram Research", title="{LocalClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_localclusteringcoefficient, organization={Wolfram Research}, title={LocalClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html}, note=[Accessed: 13-June-2026]}