Wiener number of directed graphs and its relation to the oriented network design problem.
The modified Wiener number on trees has been defined recently as a sum of modified edgecontributions, which are simply the number of shortest paths traversing the edge to the powerof . We study digraphs with minimal value for one possible modification of the Wiener numberfor directed graphs. For this generalization. For digraphs with unique shortest paths we provide minimal digraphs for 0 and 1, and give some partial results for \alpha in (0, 1).