direction = one of incoming or outgoing

When G is directed, specifies the direction of the directed path used to define which vertices of G are included in the result.

If direction=outgoing, a vertex w is included in the result if there is a directed path from some vertex in V to w. If direction=incoming, w is included in the result if there is a directed path from w to some vertex in V.

The default is direction=outgoing.

EgoGraph(G, V, dist) returns the induced subgraph of G defined by those vertices of G which are within distance dist from any of vertices referenced in V.

If G is undirected, EgoGraph(G, V, dist) returns a subgraph of G in which a vertex w is present if there exists a path from some vertex in V to w whose length is less than or equal to dist.

If G is directed, EgoGraph(G, V, dist) returns a subgraph of G in which a vertex w is present if there exists a directed path from some vertex in V to w whose length is less than or equal to dist.

If G is weighted, these paths are weighted paths.

If dist is not specified, a default value of 1 is assumed.

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

$G≔\mathrm{CycleGraph}\left(7\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 7\; vertices\; and\; 7\; edge(s)}$

$\mathrm{EgoGraph}\left(G\,1\,2\right)$

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

$\mathrm{EgoGraph}\left(G\,1\,3\right)$

$\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 7\; vertices\; and\; 7\; edge(s)}$

$\mathrm{DG}≔\mathrm{Digraph}\left(\mathrm{Trail}\left(1\,2\,3\,4\,5\,3\right)\,\mathrm{Trail}\left(1\,5\,2\,4\,1\right)\right)$

$\mathrm{DG}≔\mathrm{Graph\; 4:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 9\; arc(s)}$

$\mathrm{EgoGraph}\left(\mathrm{DG}\,2\,2\right)$

$\mathrm{Graph\; 5:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 9\; arc(s)}$

$\mathrm{EgoGraph}\left(\mathrm{DG}\,2\,2\,\mathrm{direction}=\mathrm{incoming}\right)$

$\mathrm{Graph\; 6:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 9\; arc(s)}$

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

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