Induced subgraph within distance r (default 1) of the given centers
NeighborhoodGraph[g, v]
NeighborhoodGraph[g, {a1, a2, …}]
NeighborhoodGraph[g, patt]
NeighborhoodGraph[g, …, d]
NeighborhoodGraph[{v -> w, …}, …]
g = PetersenGraph[5, 2]; HighlightGraph[g, {NeighborhoodGraph[g, 1], Labeled[1, 1]}]
→ Graph[<10>, <15>]