Neighborhood
المؤلف:
Balakrishnan, R. and Ranganathan, K.
المصدر:
"Vertex Cuts and Edge Cuts." §3.1 in A Textbook of Graph Theory. New York: Springer-Verlag
الجزء والصفحة:
...
24-7-2021
1977
Neighborhood
"Neighborhood" is a word with many different levels of meaning in mathematics.
One of the most general concepts of a neighborhood of a point 
(also called an epsilon-neighborhood or infinitesimal open set) is the set of points inside an 
-ball with center 
and radius 
. A set containing an open neighborhood is also called a neighborhood.
The graph neighborhood of a vertex 
in a graph is the set of all the vertices adjacent to 
generally 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 
(again, most commonly including 
itself) is called the neighborhood graph (or sometimes "ego graph" in more recent literature).
REFERENCES:
Balakrishnan, R. and Ranganathan, K. "Vertex Cuts and Edge Cuts." §3.1 in A Textbook of Graph Theory. New York: Springer-Verlag, p. 3, 1999.
Buckley, F. and Harary, F. Distance in Graphs. Redwood City, CA: Addison-Wesley, p. 167, 1990.
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