RandomGraph[DegreeGraphDistribution[Table[3,100]]]
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RandomGraph[DegreeGraphDistribution[Table[2,100]]]
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​
HypergraphDimensionEstimateList[List@@@EdgeList@RandomGraph[DegreeGraphDistribution[Table[3,1000]]]]
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
Log[4]
Log[2]
,2.2549±0.0014,2.718±0.004,3.254±0.008,3.792±0.013,4.273±0.018,4.541±0.022,4.415±0.024,3.590±0.022,2.035±0.016,0.548±0.007
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ListLinePlot[%]
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RandomGraph[DegreeGraphDistribution[Table[4,100]]]
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HypergraphDimensionEstimateList[List@@@EdgeList@RandomGraph[DegreeGraphDistribution[Table[4,1000]]]]
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
Log[5]
Log[2]
,3.0101±0.0013,3.902±0.004,4.753±0.007,5.209±0.011,4.452±0.011,1.845±0.008,0.1033±0.0016
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ListLinePlot[%]
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RandomGraph[DegreeGraphDistribution[Table[5,100]]]
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