Key points are not available for this paper at this time.
The results of Hakimi and Yau and others in the realization of a distance matrix are generalized to graphs (digraphs) whose branches (arcs) may have negative weights. Conditions under which such matrices have a tree, hypertree or directed tree realization are given, uniqueness of these realizations is discussed and algorithms for their construction are indicated.
Patrinos et al. (Sun,) studied this question.