EvolutionPicture2[{{1,2},{2,3}}{{4,1},{4,3},{2,1},{2,3},{4,5}},{{0,0},{0,0}},9]
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VertexOutDegree
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{1,0,2,0,3,0,3,4,0,0,2,0,0,1,0,2,0,0,2,0,0,2,2,0,2,0,3,2,7,0,2,0,2,2,0,2,0,0,3,2,0,0,1,0,3,2,0,11,1,0,3,4,0,3,0,0,3,2,0,3,0,3,4,0,3,4,0,3,0,0,3,0,3,4,0,3,0,0,3,0,3,0,0,3,8,0,3,0,3,0,0,3,0,3,0,3,0,3,0,0,3,0,3,0,0,3,0,3,0,3,0,3,0,3,0}
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Counts[%]
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14,057,215,331,45,71,111,81
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RemoveDanglingEnds[graph_]:=VertexDelete[graph,Pick[VertexList[graph],#0&/@VertexOutDegree[graph]]]
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RemoveDanglingEnds
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NeighborhoodGraph
RemoveDanglingEnds
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RemoveDanglingEndsU[graph_]:=VertexDelete[graph,Pick[VertexList[graph],#<2&/@VertexOutDegree[UndirectedGraph[graph]]]]
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RemoveDanglingEndsU
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RemoveDanglingEndsU/@
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
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RemoveDanglingEndsU[Graph[Rule@@@#,GraphLayout"SpringElectricalEmbedding",ImageSizeTiny]]&@WolframModel[{{1,2},{2,3}}{{4,1},{4,3},{2,1},{2,3},{4,5}},{{0,0},{0,0}},11,"FinalState"]
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