If v is a vertex of the graph, HasSelfLoop(G,v) returns true if the graph G has an edge or arc v to itself, and false otherwise.

The NumberOfSelfLoops(G) command returns the number of self-loops in G.

The SelfLoops(G) command returns a set of self-loops in G.

Because the data structure for a graph is an array of sets of neighbors, the test for self-loop existence checks each neighbor set and the cost is O(n) where n is the number of vertices.

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

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

$G≔\mathrm{Graph\; 1:\; a\; directed\; unweighted\; graph\; with\; 4\; vertices,\; 4\; arc(s),\; and\; 1\; self-loop(s)}$

$\mathrm{HasSelfLoop}\left(G\,2\right)$

$\mathrm{false}$

$\mathrm{HasSelfLoop}\left(G\,3\right)$

$\mathrm{true}$

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

$1$

The GraphTheory[HasSelfLoop], GraphTheory[NumberOfSelfLoops] and GraphTheory[SelfLoops] commands were introduced in Maple 2020.

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