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

The closeness centrality of a vertex v is the reciprocal of the average graph distance between v and every vertex reachable from v.

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

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

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

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

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

$\left[\frac{5}{8}\,\frac{5}{8}\,\frac{5}{8}\,\frac{5}{7}\,\frac{5}{8}\,1\right]$

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

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