gx=Graph[Rule@@@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{3,4},{4,1},{4,3}},Table[0,3,2],20,"FinalState"]]
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GraphDiameter[gx]
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∞
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GraphDiameter[UndirectedGraph[gx]]
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15
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gxall=Graph[Rule@@@#]&/@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{3,4},{4,1},{4,3}},Table[0,3,2],20,"StatesList"];
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GraphDiameter[UndirectedGraph[#]]&/@gxall
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{0,1,1,2,2,3,3,4,4,6,7,7,9,9,11,11,13,11,12,13,15}
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ListLinePlot[%]
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LoopFreeGraphQ[gx]
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False
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GraphHub[gx]
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{34}
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GraphHub[UndirectedGraph[gx]]
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{6,34}
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GraphDensity[gx]//N
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0.00379142
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GraphDensity[UndirectedGraph[gx]]//N
In[]:=
0.00637335
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N[GraphDensity[UndirectedGraph[#]]]&/@gxall
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GraphDensity
,1.,1.,0.833333,0.533333,0.464286,0.327273,0.238095,0.187135,0.144928,0.106061,0.0786268,0.0614035,0.042624,0.0337374,0.0259596,0.0197454,0.0146456,0.0111468,0.00827533,0.00637335
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ListLinePlot[Rest[%]]
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CommunityGraphPlot[UndirectedGraph[gx]]
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CommunityGraphPlot[UndirectedGraph[#]]&/@gxall
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GraphLinkEfficiency[UndirectedGraph[#]]&/@gxall//N
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GraphLinkEfficiency,0.,0.666667,0.766667,0.816667,0.876374,0.90202,0.918857,0.92818,0.93442,0.947714,0.955079,0.962636,0.968958,0.974311,0.977514,0.982455,0.986334,0.9892,0.991221,0.992923
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GraphLinkEfficiency[#]&/@gxall//N
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GraphLinkEfficiency
,0.5,0.766667,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞,-∞
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Histogram[LocalClusteringCoefficient[UndirectedGraph[gx]]]
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Histogram[ClosenessCentrality[UndirectedGraph[#]]]&/@gxall
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Histogram[BetweennessCentrality[UndirectedGraph[#]]]&/@gxall
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