Freeman’s centralization for a given centrality index is a measure of how central a vertex is regarding to how central all the other vertices are with respect to the given index. The well studied Wiener index (the Wiener number) of a graph G is equal to the sum of distances between all pairs of vertices of G . In the talk I will present the centralization of Wiener index, in particular, we will determine the graphs on n vertices which attain the maximum or minimum value.