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

The harmonic centrality of a vertex v is the sum of the reciprocal of the graph distance from u to v for every other vertex u in G.

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

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

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

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

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

$\left[\frac{7}{2}\,\frac{7}{2}\,\frac{7}{2}\,4\,\frac{7}{2}\,5\right]$

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

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