Initial data commit
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g = Graph[{1 \[DirectedEdge] 3, 3 \[DirectedEdge] 4,
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4 \[DirectedEdge] 2, 2 \[DirectedEdge] 1, 2 \[DirectedEdge] 3},
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EdgeWeight -> {(1 \[DirectedEdge] 3) -> -2, (3 \[DirectedEdge] 4) ->
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2, (4 \[DirectedEdge] 2) -> -1, (2 \[DirectedEdge] 1) ->
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4, (2 \[DirectedEdge] 3) -> 3}]
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vl = VertexList[g];
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dm = GraphDistanceMatrix[g];
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Grid[LexicographicSort[
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DeleteCases[
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Catenate[
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Table[{vl[[i]], vl[[j]], dm[[i, j]]}, {i, Length[vl]}, {j,
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Length[vl]}]], {x_, x_, _}]]]
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