output=one of graph or list

Specifies whether the result should be a list of vertices reachable from v or the subgraph induced by the vertices reachable from v. The default is list.

Ancestors(G,v) returns a list of all ancestors of v in G, that is, vertices in G from which v is reachable.

Descendants returns a list of all descendants of v in G, that is, vertices in G which are reachable from the vertex v.

Note that the input vertex v is excluded from the output, even if the graph contains a loop including v.

To produce an actual spanning tree of vertices reachable from v, see SpanningTree or MinimalSpanningTree.

If G is a directed graph and there exists a directed path in G from u to v, then u is said to be an ancestor of v, and v is said to be descendant of u.

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

$\mathrm{C6}≔\mathrm{CycleGraph}\left(6\,\mathrm{directed}\right)$

$\mathrm{C6}≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 6\; vertices\; and\; 6\; arcs}$

$\mathrm{DrawGraph}\left(\mathrm{C6}\right)$

$\mathrm{Ancestors}\left(\mathrm{C6}\,6\right)$

$\left[1\,2\,3\,4\,5\right]$

$\mathrm{Ancestors}\left(\mathrm{C6}\,6\,\mathrm{output}=\mathrm{graph}\right)$

$\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 4\; arcs}$

$T≔\mathrm{Graph}\left(5\,\left\{\left[1\,2\right]\,\left[1\,4\right]\,\left[2\,3\right]\,\left[4\,5\right]\right\}\right)$

$T≔\mathrm{Graph\; 3:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 4\; arcs}$

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

$\mathrm{Ancestors}\left(T\,4\right)$

$\left[1\right]$

$\mathrm{Descendants}\left(T\,4\right)$

$\left[5\right]$

The GraphTheory[Ancestors] and GraphTheory[Descendants] commands were introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.