GraphCenter

GraphCenter[g] gives the set of vertices with minimum eccentricity (most central vertices) in graph g.

Examples

Center of a path:

GraphCenter[PathGraph[Range[5]]]
(* {3} - middle vertex *)

Center of a cycle:

GraphCenter[CycleGraph[6]]
(* {1, 2, 3, 4, 5, 6} - all vertices *)

Center of a grid:

GraphCenter[GridGraph[{3, 3}]]
(* {5} - center of 3x3 grid *)

Please visit the official Wolfram Language Reference for more details.