The center of a graph 
is the set of vertices of graph
eccentricity equal to the graph radius (i.e.,
the set of central points). In the above illustration,
center nodes are shown in red.
The center of a graph may be computed in the Wolfram
Language with the command GraphCenter[g].
The following table gives the number of 
-node simple unlabeled graphs having 
center nodes.
 | OEIS |  , 2, ... |
| 1 | A052437 | 1,
0, 1, 2, 8, 29, 180, ... |
| 2 | A052438 | 0, 2, 0, 2, 4, 19,
84, ... |
| 3 | A052439 | 0, 0, 3, 0, 4, 18, 119, ... |
| 4 | A052340 | 0,
0, 0, 7, 0, 18, 118, ... |
| 5 | A052341 | 0, 0, 0, 0, 18, 0,
129, ... |
| 6 | | 0,
0, 0, 0, 0, 72, 0, ... |
| 7 | | 0, 0, 0, 0, 0, 0, 414, ... |
See also
Bicentered Tree,
Central Point,
Centered Tree,
Graph
Eccentricity,
Graph Periphery,
Graph
Radius
Explore with Wolfram|Alpha
References
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35, 1994.Skiena,
S. Implementing
Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading,
MA: Addison-Wesley, p. 107, 1990.Sloane, N. J. A. Sequences
A052437, A052438,
A052439, A052340,
and A052341 in "The On-Line Encyclopedia
of Integer Sequences."Referenced on Wolfram|Alpha
Graph Center
Cite this as:
Weisstein, Eric W. "Graph Center." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphCenter.html
Subject classifications
