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GraphTheory

  

InformationCentrality

  

compute information centrality

 

Calling Sequence

Parameters

Description

Definition

Examples

References

Compatibility

Calling Sequence

InformationCentrality(G)

InformationCentrality(G, v)

Parameters

G

-

graph

v

-

(optional) a vertex of G

Description

• 

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

Definition

• 

Let G be a graph with vertex set V of size n, and let L be the Laplacian matrix of G.

• 

Define B to be the matrix inverse of L+J, where J represents the n by n matrix in which every entry is 1.

• 

Then the information centrality IC(v) of a vertex v in G is defined as

ICv=nuVBu,uBv,v2Bu,v

Examples

withGraphTheory:

Compute the information 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

InformationCentralityG

7261,3629,7261,7249,3629,7237

(2)

References

  

K. Stephenson and M. Zelen. "Rethinking centrality: Methods and examples." Social Networks, 11(1):1–37, 1989. doi:10.1016/0378-8733(89)90016-6

  

L. Shan, Y. Yi, Z. Zhang, "Improving Information Centrality of a Node in Complex Networks by Adding Edges", Proc IJCAI 2018. doi:10.24963/ijcai.2018/491

Compatibility

• 

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

• 

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

See Also

BetweennessCentrality

ClosenessCentrality

DegreeCentrality

EigenvectorCentrality

HarmonicCentrality

KatzCentrality

PageRankCentrality