The Subdivide command subdivides the specified edges or arcs of a graph or digraph, by putting r new vertices on each specified edge or arc.

If r is not specified, a default value of 1 is used.

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

$G≔\mathrm{CompleteGraph}\left(2\,3\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 6\; edge(s)}$

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

$\left\{\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{1\,5\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\right\}$

$\mathrm{SG}≔\mathrm{Subdivide}\left(G\,\left\{\left\{1\,5\right\}\,\left\{2\,4\right\}\right\}\right)$

$\mathrm{SG}≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 7\; vertices\; and\; 8\; edge(s)}$

$\mathrm{Edges}\left(\mathrm{SG}\right)$

$\left\{\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{1\,6\right\}\,\left\{2\,3\right\}\,\left\{2\,5\right\}\,\left\{2\,7\right\}\,\left\{4\,7\right\}\,\left\{5\,6\right\}\right\}$

$\mathrm{DG}≔\mathrm{Digraph}\left(\left[a\,b\,c\right]\,\left\{\left[a\,b\right]\,\left[a\,c\right]\right\}\right)$

$\mathrm{DG}≔\mathrm{Graph\; 3:\; a\; directed\; unweighted\; graph\; with\; 3\; vertices\; and\; 2\; arc(s)}$

$\mathrm{Edges}\left(\mathrm{DG}\right)$

$\left\{\left[a\,b\right]\,\left[a\,c\right]\right\}$

$\mathrm{SDG}≔\mathrm{Subdivide}\left(\mathrm{DG}\,\left[a\,b\right]\,2\right)$

$\mathrm{SDG}≔\mathrm{Graph\; 4:\; a\; directed\; unweighted\; graph\; with\; 5\; vertices\; and\; 4\; arc(s)}$

$\mathrm{Edges}\left(\mathrm{SDG}\right)$

$\left\{\left[1\,2\right]\,\left[2\,b\right]\,\left[a\,1\right]\,\left[a\,c\right]\right\}$