# LocalClusteringCoefficient

gives the list of local clustering coefficients of all vertices in the graph g.

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: