GraphTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


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

GraphTheory

  

KatzCentrality

  

compute Katz centrality

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

KatzCentrality(G, alpha, )

KatzCentrality(G, alpha, v)

Parameters

G

-

graph

alpha

-

real constant

v

-

(optional) a vertex of G

Description

• 

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

• 

Katz centrality computes the relative influence of a vertex within a network by measuring the number of the immediate neighbors and also all other reachable vertices. Connections made with distant vertex are, however, penalized by an attenuation factor alpha.

Examples

withGraphTheory:

Compute the Katz 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

KatzCentralityG,0.1

1.29598461168550,1.30920894445780,1.29598461168550,1.42822793940851,1.30920894445780,1.66386150516951

(2)

Compatibility

• 

The GraphTheory[KatzCentrality] 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

InformationCentrality

PageRankCentrality