The GraphDensity(G) command returns the graph density of G.

For an undirected graph with n vertices and m edges, the graph density is $\frac{2m}{n\left(n-1\right)}$.

For a directed graph with n vertices and m arcs, the graph density is $\frac{m}{n\left(n-1\right)}$.

Note that self-loops are not included in the edge count for the purposes of computing graph density.

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

$\mathrm{K4}≔\mathrm{CompleteGraph}\left(4\right)$

$\mathrm{K4}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 6\; edge(s)}$

$\mathrm{GraphDensity}\left(\mathrm{K4}\right)$

$1$

$H≔\mathrm{Digraph}\left(\mathrm{Trail}\left(1\,2\,3\,1\,4\,3\right)\,\mathrm{Trail}\left(4\,2\,1\,3\right)\right)\:$

$\mathrm{GraphDensity}\left(H\right)$

$\frac{2}{3}$

The GraphTheory[GraphDensity] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.