EnumerateHypergraphs[{{2,3}}]
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ParallelMapMonitored[#->FindCanonicalHypergraph[Map[#[[{3,2,1}]]&,#,{1}]]&,EnumerateHypergraphs[{{2,3}}]]
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Graph[%]
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This is additional isomorphism beyond hypergraph isomorphism, and it’s not very important....
Function[perm,ParallelMapMonitored[#->FindCanonicalHypergraph[Map[#[[perm]]&,#,{1}]]&,EnumerateHypergraphs[{{2,3}}]]]/@Rest[Permutations[Range[3]]]
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Graph/@%
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Function[perm,Graph[ParallelMapMonitored[#->FindCanonicalHypergraph[Map[#[[perm]]&,#,{1}]]&,EnumerateHypergraphs[{{3,3}}]]]]/@Rest[Permutations[Range[3]]]
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Strings

Graph[#Reverse[#]&/@Tuples[{1,0},4]]
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Graph[#Reverse[#]&/@Tuples[{2,1,0},4]]
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Graph[#RotateLeft[#]&/@Tuples[{1,0},4]]
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LHS of rule can be permuted....