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 Resource. https://mathworld.wolfram.com/GraphCenter.html
Subject classifications
