Neighborhood Graph

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].

REFERENCES

Newman, M. Networks: An Introduction. Oxford, England: Oxford University Press, 2010.