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GraphTheory

  

EigenvectorCentrality

  

compute eigenvector centrality

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

EigenvectorCentrality(G)

EigenvectorCentrality(G, v)

Parameters

G

-

graph

v

-

(optional) a vertex of G

Description

• 

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

• 

Let A be the adjacency matrix of G. The eigenvector centrality of a vertex v in G is the normalized value of the corresponding entry in the eigenvector of A which corresponds with the largest eigenvalue of A.

Examples

withGraphTheory:

Compute the eigenvector 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

EigenvectorCentralityG

0.130085678713417,0.149538495378514,0.130085678713417,0.187421156483979,0.149538495378514,0.253330495332159

(2)

Compatibility

• 

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

• 

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

See Also

BetweennessCentrality

ClosenessCentrality

DegreeCentrality

HarmonicCentrality

InformationCentrality

KatzCentrality

PageRankCentrality