GraphTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Discrete Mathematics : Graph Theory : GraphTheory Package : GraphTheory/LocalClusteringCoefficient

GraphTheory

  

LocalClusteringCoefficient

  

compute local clustering coefficient

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

LocalClusteringCoefficient(G)

LocalClusteringCoefficient(G, v)

Parameters

G

-

graph

v

-

(optional) a vertex of G

Description

• 

LocalClusteringCoefficient returns the local clustering coefficient for the given graph G.

• 

The local clustering coefficient is a number between 0 and 1 measuring how close the neighborhood of v is to a clique.

• 

For a node v with n neighbors, the local cluster coefficient is the simply the number of edges between neighbors of v (counting undirected edges twice) and the number nn1, which is the maximum number of (directed) edges possible between n neighbors.

Examples

withGraphTheory:

GGraph1,2,3,4,5,6,1,3,1,6,2,6,2,4,3,6,4,6,4,5,5,6

GGraph 1: an undirected unweighted graph with 6 vertices and 8 edge(s)

(1)

DrawGraphG

Compute the clustering coefficient for vertex 6

LocalClusteringCoefficientG,6

310

(2)

Produce a list of all local clustering coefficients

LocalClusteringCoefficientG

111231310

(3)

Compatibility

• 

The GraphTheory[LocalClusteringCoefficient] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

GlobalClusteringCoefficient