The edge-Wiener index of a graph

If G is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of G. The edge-Wiener index W"e of G is then equal to the sum of distances between all pairs of edges of G. We give bounds on W"e in terms of order and size. In particular we prove the asymptotically sharp upper bound W"e(G)@?2^55^5n^5+O(n^9^/^2) for graphs of order n.