FusionAtlasPaths={"~/projects/fusionatlas/code/package/"};
$Path=$Path~Join~FusionAtlasPaths;
<<FusionAtlas`

AH2=GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,1,0},{0,1,1}},{{0,0,1}}]

p=FindGraphPartners[AH2]

DisplayBigraph[AH2]

SetDebugMode[True]

PermuteVerticesAtDepth[g_GradedBigraph,k_,p_]:=Module[{l=List@@g},
GradedBigraph@@(If[k>0,Take[l,k-1],{}]~Join~If[k>0,{l[[k,p]]},{}]~Join~If[k<GraphDepth[g],{l[[k+1,All,p]]},{}]~Join~If[k<GraphDepth[g],Drop[l,k+1],{}])
]

AllPermutationsAtDepth[g_GradedBigraph,k_]:=Union[PermuteVerticesAtDepth[g,k,#]&/@Permutations[Range[RankAtDepth[g,k]]]]
AllPermutationsAtDepth[l:{___GradedBigraph},k_]:=Union[Flatten[AllPermutationsAtDepth[#,k]&/@l,1]]

AllOddPermutations[g_GradedBigraph]:=Fold[AllPermutationsAtDepth,g,Range[1,GraphDepth[g],2]]

DisplayBigraph/@AllOddPermutations[AH2]

BigraphWithDuals[g_GradedBigraph]:=Flatten[Function[g1,BigraphWithDuals[g1,#]&/@CompatibleDualDataList[g1]]/@AllOddPermutations[g],1]

DisplayBigraph/@BigraphWithDuals[AH2]

p2=Flatten[BigraphWithDuals/@p,1];

p3=Cases[Flatten[Outer[List,BigraphWithDuals[AH2],p2],1],{a_,b_}/;FullOcneanuTest[a,b]];

p3=FusionAtlas`PairOdometer`Private`ChooseIsomorphismRepresentatives[p3]

DisplayBigraph/@p3