Proximity and average eccentricity of a graph

Let G=(V,E) be a connected graph on n vertices. The proximity@p(G) of G is the minimum average distance from a vertex of G to all others. The eccentricitye(v) of a vertex v in G is the largest distance from v to another vertex, and the average eccentricity ecc(G) of the graph G is 1n@?"v"@?"V"("G")e(v). Recently, it was conjectured by Aouchiche and Hansen (2011) [3] that for any connected graph G on n>=3 vertices, ecc(G)-@p(G)=