VertexComponent

VertexComponent[g,{v1,v2,…}] gives the vertices in the graph g that have a path to at least one of v1, v2, ….

VertexComponent[g,{v1,v2,…},k] gives the vertices with a path to at least one of v1, v2, … of at most length k.

VertexComponent[g,{v1,v2,…},{k}] gives the vertices at length exactly k.

VertexComponent[{v->w,…},…] uses rules v->w to specify the graph g.

Examples

VertexComponent[Graph[{1 -> 2, 2 -> 3, 3 -> 4}], {1}]
(* {1, 2, 3, 4} *)

VertexComponent[Graph[{1 -> 2, 2 -> 3, 3 -> 4}], {1}, 2]
(* {1, 2, 3} *)

Please visit the official Wolfram Language Reference for more details.