The neighborhood graph of a given graph from a vertex 
is the subgraph induced by the
neighborhood of a graph from vertex 
, most commonly including 
itself. Such graphs are sometimes also known in more recent
literature as ego graphs or ego-centered networks (Newman 2010, pp. 44-46).
A graph 
for which the neighborhood graph at each point excluding the point itself
is isomorphic to a graph 
is said to be a local H graph,
or simply "locally 
."
Neighborhood graphs are implemented in the Wolfram Language as NeighborhoodGraph[g, v].
