The center of a graph G 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 n-node simple unlabeled graphs having k center nodes.

bicentered tree | centered tree | central point | graph eccentricity | graph periphery | graph radius

GraphCenter