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CloudGet["https://wolfr.am/PJKo9Lnq"];​​ReverseGraph[EuclidGraphSmall[Subgraph[euc,VertexOutComponent[euc,<|"Book"->1,"Theorem"->48|>]],"Intense"],VertexSize1,VertexStyle->(#->EuclidVertexStyle[#,"Intense"]&/@VertexList[euc]),VertexLabels->(#->EuclidVertexName[#]&/@VertexList[euc])]
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VertexList[%]
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{Book1,Theorem48,Common Notion1,Common Notion2,Book1,Theorem11,Book1,Theorem3,Book1,Theorem47,Book1,Theorem8,Postulate1,Book1,Theorem1,Book1,Theorem2,Postulate3,Book1,Theorem14,Book1,Theorem31,Book1,Theorem4,Book1,Theorem41,Book1,Theorem46,Postulate4,Common Notion4,Book1,Theorem7,Common Notion3,Postulate2,Book1,Theorem13,Book1,Theorem23,Book1,Theorem27,Book1,Theorem34,Book1,Theorem37,Book1,Theorem29,Common Notion5,Book1,Theorem5,Book1,Theorem22,Book1,Theorem16,Book1,Theorem26,Book1,Theorem35,Book1,Theorem15,Postulate5,Book1,Theorem20,Book1,Theorem10,Book1,Theorem19,Book1,Theorem9,Book1,Theorem18}
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DeleteCases[%,<|"Book"->_,__|>]
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{Common Notion1,Common Notion2,Postulate1,Postulate3,Postulate4,Common Notion4,Common Notion3,Postulate2,Common Notion5,Postulate5}
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Length[%]
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10
[[[ Most theorems depend on all axioms .... representing knitting together of metamathematical space ]]] [ in our reference frame, things are well knitted together ] [ our populated places are well connected ]
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VertexCount[euc]
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475
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dm=GraphDistanceMatrix[UndirectedGraph[euc]];
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MatrixPlot[dm]
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MatrixPlot[GraphDistanceMatrix[euc]]
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MatrixPlot[GraphDistanceMatrix[ReverseGraph[euc]]]
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Dimension