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GraphTheory

  

BetweennessCentrality

  

compute betweenness centrality

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

BetweennessCentrality(G)

BetweennessCentrality(G, v)

Parameters

G

-

graph

v

-

(optional) a vertex of G

Description

• 

BetweennessCentrality returns the betweenness centrality for a specified vertex in the given graph G, or if no vertex is specified, returns a list of the betweenness centralities for each vertex in G.

• 

The betweenness centrality of a vertex v is a measure of the proportion of shortest paths through the graph which pass through v. It is the sum over all pairs of vertices a and b (both different from v) of the number of least-weight paths from a to b which pass through v divided by the total number of least-weight paths from a to b.

Examples

withGraphTheory:

Compute the betweenness centrality for a specified graph.

GGraph6,1,3,1,6,2,4,2,6,3,6,4,5,4,6,5,6

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

(1)

DrawGraphG

BetweennessCentralityG,6

132

(2)

BetweennessCentralityG

0,0,0,12,0,132

(3)

Compatibility

• 

The GraphTheory[BetweennessCentrality] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

ClosenessCentrality

DegreeCentrality

EigenvectorCentrality

HarmonicCentrality

InformationCentrality

KatzCentrality

PageRankCentrality