KatzCentrality - Maple Help

GraphTheory

 KatzCentrality
 compute Katz centrality

 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 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

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$

Compute the Katz centrality for a specified graph.

 > $G≔\mathrm{Graph}\left(6,\left\{\left\{1,3\right\},\left\{1,6\right\},\left\{2,4\right\},\left\{2,6\right\},\left\{3,6\right\},\left\{4,5\right\},\left\{4,6\right\},\left\{5,6\right\}\right\}\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 6 vertices and 8 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{KatzCentrality}\left(G,0.1\right)$
 $\left[{1.29598461168550}{,}{1.30920894445780}{,}{1.29598461168550}{,}{1.42822793940851}{,}{1.30920894445780}{,}{1.66386150516951}\right]$ (2)

Compatibility

 • The GraphTheory[KatzCentrality] command was introduced in Maple 2020.