The graph neighborhood of a vertex 
in a graph is the set of all the
vertices adjacent to 
including 
itself. More generally, the 
th neighborhood of 
is the set of all vertices that lie at the distance 
from 
.
The subgraph induced by the neighborhood of a graph from vertex 
is called the neighborhood graph.
Note that while "graph neighborhood" generally includes vertices adjacent to 
together with the vertex 
itself, the term "graph neighbors" generally means
vertices adjacent to 
excluding 
itself (e.g., Brouwer et al. 1989), so some care is
needed when encountering these terms.
