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.

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

$G≔\mathrm{Graph}\left(6\,\left\{\left\{1\,3\right\}\,\left\{1\,6\right\}\,\left\{2\,4\right\}\,\left\{2\,6\right\}\,\left\{3\,6\right\}\,\left\{4\,5\right\}\,\left\{4\,6\right\}\,\left\{5\,6\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 8\; edge(s)}$

$\mathrm{DrawGraph}\left(G\right)$

$\mathrm{KatzCentrality}\left(G\,0.1\right)$

$\left[1.29598461168550\,1.30920894445780\,1.29598461168550\,1.42822793940851\,1.30920894445780\,1.66386150516951\right]$

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

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