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

open allclose all

Basic Examples  (2)

Find the mean clustering coefficient of a graph:

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

Scope  (5)

MeanClusteringCoefficient works with undirected graphs:

Directed graphs:

Multigraphs:

Use rules to specify the graph:

MeanClusteringCoefficient works with large graphs:

Applications  (2)

Mean clustering coefficient of a power grid network:

Compare to uniform random graphs:

Collaboration networks tend to have high mean clustering coefficients:

Compare to uniform random graphs:

Properties & Relations  (7)

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

The mean clustering coefficient is between 0 and 1:

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

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

Distribution of mean clustering coefficient in BernoulliGraphDistribution:

Expected value:

Distribution of mean 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 mean clustering coefficient in BarabasiAlbertGraphDistribution:

Compare with GlobalClusteringCoefficient:

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_2024_meanclusteringcoefficient, author="Wolfram Research", title="{MeanClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_meanclusteringcoefficient, organization={Wolfram Research}, title={MeanClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}, note=[Accessed: 21-November-2024 ]}