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We consider the problem of computing all-pairs shortest paths in a directed graph with non-negative real weights assigned to vertices. For an n ×n 0−1 matrix C , let K C be the complete weighted graph on the rows of C where the weight of an edge between two rows is equal to their Hamming distance. Let MWT (C ) be the weight of a minimum weight spanning tree of K C . We show that the all-pairs shortest path problem for a directed graph G on n vertices with non-negative real weights and adjacency matrix A G can be solved by a combinatorial randomized algorithm in time $$\widetilde{O}(n^{2}\sqrt{n + \min\{MWT(A_G), MWT(A_G^t)\}})$$ As a corollary, we conclude that the transitive closure of a directed graph G can be computed by a combinatorial randomized algorithm in the aforementioned time. We also conclude that the all-pairs shortest path problem for vertex-weighted uniform disk graphs induced by point sets of bounded density within a unit square can be solved in time $\widetilde{O}(n^{2.75})$ .