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g15=Graph[Rule@@@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{3,4},{4,1},{4,3}},Table[0,3,2],15,"FinalState"]]
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{x[i],y[i]}
NMinimize
GraphDistanceMatrix[UndirectedGraph[g15]]^2
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VertexCount[%]
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128
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MatrixPlot[1/(GraphDistanceMatrix[g15]/.0None)]
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MatrixPlot[1/(GraphDistanceMatrix[UndirectedGraph[g15]]/.0None)]
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MatrixPlot[Exp[-(GraphDistanceMatrix[UndirectedGraph[g15]]/.0None)]]
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MatrixPlot[1/%]
1
0
1
0
1
0
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[[[[ More to do, e.g. with manifold reconstruction ]]]]
[[[[ More to do, e.g. with manifold reconstruction ]]]]