The edge-Wiener index of a graph

If GG is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of GG. The edge-Wiener index WeWe of GG is then equal to the sum of distances between all pairs of edges of GG. We give bounds on WeWe in terms of order and size. In particular we prove the asymptotically sharp upper bound We(G)≤2555n5+O(n9/2) for graphs of order nn.