GlobalClusteringCoefficient

GlobalClusteringCoefficient[g]

gives the global clustering coefficient of the graph g.

GlobalClusteringCoefficient[{vw,}]

uses rules vw to specify the graph g.

Details

  • GlobalClusteringCoefficient is also known as clustering coefficient.
  • The global clustering coefficient of g is the fraction of paths of length two in g that are closed over all paths of length two in g.
  • GlobalClusteringCoefficient works with undirected graphs, directed graphs, and multigraphs.

Examples

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Basic Examples  (2)

Find the global clustering coefficient of a graph:

Global clustering coefficient of the WattsStrogatz model as a function of rewiring probability:

Scope  (5)

GlobalClusteringCoefficient works with undirected graphs:

Directed graphs:

Multigraphs:

Use rules to specify the graph:

GlobalClusteringCoefficient works with large graphs:

Properties & Relations  (6)

The global clustering coefficient is between 0 and 1:

The global clustering coefficient for a graph with no paths of length two is 0:

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

Distribution of global clustering coefficient in BernoulliGraphDistribution:

Expected value:

Distribution of a global clustering coefficient in WattsStrogatzGraphDistribution:

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

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

Distribution of a global clustering coefficient in BarabasiAlbertGraphDistribution:

Compare with MeanClusteringCoefficient:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_globalclusteringcoefficient, author="Wolfram Research", title="{GlobalClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GlobalClusteringCoefficient.html}", note=[Accessed: 24-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_globalclusteringcoefficient, organization={Wolfram Research}, title={GlobalClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/GlobalClusteringCoefficient.html}, note=[Accessed: 24-October-2021 ]}

CMS

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

APA

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