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The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let G = G(V, E) be an undirected graph with the set of vertices V and the set of edges E. A necessary and sufficient condition under which the weight w : E → R + on the graph G has a unique continuation to a metric d : V × V → R + is found.doi:10.20429/tag.2022.100101 fatcat:eckbkfb3b5df5awd6ac67unlqi