Basic Examples (from EdP)

EnumerateHypergraph[lhs_,opts:OptionsPattern[]]:=First/@EnumerateWolframModelRules[lhs{},{maxConnectedAtoms[lhs{},Automatic],Automatic},opts]
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EnumerateHypergraph[lhs_,type:Automatic|None|All,opts:OptionsPattern[]]:=First/@EnumerateWolframModelRules[lhs{},{maxConnectedAtoms[lhs{},type],type},opts]
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EnumerateHypergraph[lhs_,s_Integer,opts:OptionsPattern[]]:=First/@EnumerateWolframModelRules[lhs{},{s,Automatic},opts]
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EnumerateHypergraph[{{3,2}}]
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Graph[DirectedEdge@@@#,ImageSizeTiny,GraphLayout"SpringElectricalEmbedding"]&/@EnumerateHypergraph[{{3,2}}]
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Union[Graph[DirectedEdge@@@#,ImageSizeTiny,GraphLayout"SpringElectricalEmbedding"]&/@EnumerateHypergraph[{{3,2}}],SameTest(IsomorphicGraphQ[UndirectedGraph[#1],UndirectedGraph[#2]]&)]
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Union[Graph[DirectedEdge@@@#,ImageSizeTiny,GraphLayout"SpringElectricalEmbedding"]&/@EnumerateHypergraph[{{4,2}}],SameTest(IsomorphicGraphQ[UndirectedGraph[#1],UndirectedGraph[#2]]&)]
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Graph[DirectedEdge@@@#,ImageSizeTiny,GraphLayout"SpringElectricalEmbedding"]&/@EnumerateHypergraph[{{4,2}}]
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HypergraphPlot[#,ImageSizeTiny]&/@EnumerateHypergraph[{{2,3}}]
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HypergraphPlot[#,ImageSizeTiny]&/@Union[EnumerateHypergraph[{{2,3}}],SameTest(IsomorphicGraphQ[UndirectedGraph[HypergraphToGraph@#1],UndirectedGraph[HypergraphToGraph@#2]]&)]
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HypergraphPlot[#,ImageSizeTiny]&/@Union[EnumerateHypergraph[{{2,2}}],SameTest(IsomorphicGraphQ[UndirectedGraph[HypergraphToGraph@#1],UndirectedGraph[HypergraphToGraph@#2]]&)]
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HypergraphPlot[#,ImageSizeTiny]&/@Union[EnumerateHypergraph[{{3,2}}],SameTest(IsomorphicGraphQ[UndirectedGraph[HypergraphToGraph@#1],UndirectedGraph[HypergraphToGraph@#2]]&)]
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Map[{Echo@#->Length[EnumerateHypergraphs[{#}]]}&,{{1,2},{2,2},{3,2},{4,2},{5,2},{1,3},{2,3},{3,3},{4,3}}]
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{1,2}
»
{2,2}
»
{3,2}
»
{4,2}
»
{5,2}
»
{1,3}
»
{2,3}
»
{3,3}
»
{4,3}
»
{{{1,2}1},{{2,2}5},{{3,2}24},{{4,2}140},{{5,2}837},{{1,3}4},{{2,3}96},{{3,3}3231},{{4,3}164070}}
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Flatten[%]
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{{1,2}1,{2,2}5,{3,2}24,{4,2}140,{5,2}837,{1,3}4,{2,3}96,{3,3}3231,{4,3}164070}
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Association[%]
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{1,2}1,{2,2}5,{3,2}24,{4,2}140,{5,2}837,{1,3}4,{2,3}96,{3,3}3231,{4,3}164070
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FindSequenceFunction[{1,5,24,140},n]
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FindSequenceFunction[{1,5,24,140},n]
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Map[{#,Echo@Length[EnumerateHypergraph[{#}]]}&,Table[{n,2},{n,6}]]
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1
»
5
»
24
»
140
»
837
»
5574
»
{{{1,2},1},{{2,2},5},{{3,2},24},{{4,2},140},{{5,2},837},{{6,2},5574}}
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Last/@%
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{1,5,24,140,837,5574}
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FindSequenceFunction[%,n]
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FindSequenceFunction[{1,5,24,140,837,5574},n]
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EnumerateHypergraphs[{{1,3}}]
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{{{1,1,1}},{{1,1,2}},{{1,2,1}},{{1,2,2}}}
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Map[EchoFunction[{Now,#}&][#->Length[EnumerateHypergraphs[{#}]]]&,Table[{i,j},{j,2,4},{i,5}],{2}]
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
Wed 25 Dec 2019 00:45:24GMT-5.
,{1,2}1
»

Wed 25 Dec 2019 00:45:24GMT-5.
,{2,2}5
»

Wed 25 Dec 2019 00:45:24GMT-5.
,{3,2}24
»

Wed 25 Dec 2019 00:45:24GMT-5.
,{4,2}140
»

Wed 25 Dec 2019 00:45:31GMT-5.
,{5,2}837
»

Wed 25 Dec 2019 00:45:31GMT-5.
,{1,3}4
»

Wed 25 Dec 2019 00:45:31GMT-5.
,{2,3}96
»

Wed 25 Dec 2019 00:45:32GMT-5.
,{3,3}3231
»

Wed 25 Dec 2019 00:47:35GMT-5.
,{4,3}164070
»
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