The closed neighborhood of a graph vertex 
in a graph 
is the set
![N[v]={v} union {u:uv in E(G)},](/images/equations/ClosedNeighborhood/NumberedEquation1.svg) |
consisting of 
together with every vertex adjacent to 
. Under a common convention it is also
called the graph neighborhood of 
, although some authors use "neighborhood" for the
open graph neighborhood 
instead.
Two adjacent vertices are true twins exactly when they have the same closed neighborhood.
