The distance matrix of a graph and its tree realization
A. N. Patrinos, S. L. Hakimi · Quarterly of Applied Mathematics · 1972
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.