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:

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:

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