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bd = Graph[{"a" \[DirectedEdge] "b", "a" \[DirectedEdge] "c",
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"b" \[DirectedEdge] "c", "b" \[DirectedEdge] "d",
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"c" \[DirectedEdge] "d", "d" \[DirectedEdge] "e",
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"a" \[DirectedEdge] "f", "c" \[DirectedEdge] "f",
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"e" \[DirectedEdge] "f"},
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EdgeWeight -> {7, 9, 10, 15, 11, 6, 14, 2, 9},
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VertexLabels -> "Name", VertexLabelStyle -> Directive[Black, 20],
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ImagePadding -> 20]
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FindShortestPath[bd, "a", "e", Method -> "Dijkstra"]
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-> {"a", "c", "d", "e"}
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