On the Minimum Spanning Tree for Directed Graphs with Potential Weights
  In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected graphs cannot usually be applied to the directed case. In this paper we examine the kind of weights such that the problems are equivalent and a minimum spanning tree of a directed graph may be found by a simple algorithm for an undirected graph. 
V. A. Buslov, V. A. Khudobakhshov