9
To get neighboring vertices I first tried:
gg = GridGraph[{10, 10, 10, 10}];
VertexList[NeighborhoodGraph[gg, 1, 1]] // AbsoluteTiming
{5.539308, {1, 2, 11, 101, 1001}}
But that is really slow. This is much faster and still uses the new Graph package:
Union[VertexInComponent[gg, 1, 1],...