  In this article we introduce a general definition of the concept of center of
an $n$-gon, for $n\geq 3$, generalizing the idea of C. Kimberling for triangle.
We define centers associated to functions instead of to geometrical properties.
We discuss the definition of those functions depending on both, the vertices of
the polygons or the lengths of sides and diagonals. We explore the problem of
characterization of regular polygons in terms of these $n$-gon center functions
and we study the relation between our general definition of center of a polygon
and other approaches arising from Applied Mathematics.
