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

open allclose all

Basic Examples  (2)

Compute local clustering coefficients:

Highlight:

Distribution of local clustering coefficients in a graph:

Scope  (6)

LocalClusteringCoefficient works with undirected graphs:

Directed graphs:

Multigraphs:

Find the local clustering coefficient of a vertex:

Use rules to specify the graph:

LocalClusteringCoefficient works with large graphs:

Applications  (2)

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

Plot the mean as a function of the vertex degree:

Local clustering coefficients of Zachary's Karate Club:

Highlight vertices based on their local clustering coefficients:

Properties & Relations  (4)

The local clustering coefficients take values between 0 and 1:

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

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

MeanClusteringCoefficient gives the mean of 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).

BibTeX

@misc{reference.wolfram_2021_localclusteringcoefficient, author="Wolfram Research", title="{LocalClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html}", note=[Accessed: 27-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_localclusteringcoefficient, organization={Wolfram Research}, title={LocalClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html}, note=[Accessed: 27-November-2021 ]}

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