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:

Mean clustering coefficient in the WattsStrogatz 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:

Introduced in 2012
 (9.0)
 |
Updated in 2014
 (10.0)
2015
 (10.3)