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

SymmetricMatrices[n_]:=With[{t=n(n+1)/2},
Flatten[Table[Table[a@@Sort[{i,j}],{i,1,n},{j,1,n}],Evaluate[Sequence@@Flatten[Table[{a[i,j],0,1},{i,1,n},{j,i,n}],1]]],t-1]]

ConnectedSymmetricMatrices[n_]:=DeleteCases[SymmetricMatrices[n],M_/;MemberQ[M,ZeroVector[n]]]

MatrixForm/@ConnectedSymmetricMatrices[2]

PermutationSymmetricMatrices[n_]:=Union[Flatten[Outer[#1[[#2]]&,ConnectedSymmetricMatrices[n],Permutations[Range[n]],1],1]]

m=ConnectedSymmetricMatrices[3][[-3]]

GradedBigraph[M_,p_]=.

GradedBigraph[M_?MatrixQ,p_Integer]:=Module[{n,MM,V,depths},
n=Length[M];
MM=ArrayFlatten[{{ZeroMatrix[n],M},{Transpose[M],ZeroMatrix[n]}}];
V[-1]={};
V[0]={p};V[k_]:=Complement[Flatten[Position[Plus@@(MM.UnitVector[2 n,#]&/@V[k-1]),m_/;m>0]],V[k-2]];
depths=TakeWhile[Table[V[k],{k,0,2n-1}],Length[#]>0&];
GradedBigraph@@Table[MM[[depths[[i+1]],depths[[i]]]],{i,1,Length[depths]-1}]
]

GradedBigraph[m,1]

SymmetricBigraphs[n_]:=SymmetricBigraphs[n]=Union[CanonicalizeBigraph/@Cases[Union[Flatten[Outer[GradedBigraph[#1,#2]&,PermutationSymmetricMatrices[n],Range[2n],1],1]],g_/;GraphRank[g]==2n∧g[[1]]=={{1}}]]

DisplayBigraph/@SymmetricBigraphs[2]

DisplayBigraph/@SymmetricBigraphs[3]

DisplayBigraph/@SymmetricBigraphs[4]

SymmetricBigraphs[3][[2]]

DisplayBigraph[%]

gg=GradedBigraph[{{1}},{{b},{a}},{{0,1},{c,b}}]

N@(Sqrt[59/2])

Cases[Flatten[Table[{a,b,c},{a,1,5},{b,1,4},{c,1,5}],2],{a0_,b0_,c0_}/;((KnownObstructions[gg/.{a->a0,b->b0,c->c0}])=={})]

KnownObstructions[gg/.{a->1,b->1,c->1}]

N@DimensionsByDepth[gg/.Thread[{a,b,c}->#]]&/@%124//TableForm

N@GlobalEvenDimension[gg/.Thread[{a,b,c}->#]]&/@%124//TableForm

N[GlobalEvenDimension[gg/.{a->1,b->1,c->1}]]

Length[%]

Table[N@DimensionOfGenerator[gg],{a,1,3},{b,1,3},{c,1,3}]//MatrixForm

N/@DimensionsByDepth/@(Table[gg,{a,1,10}]/.{a->1,b->1,c->1,d->1,e->1,f->1,g->1})

Eigenvalues[GraphAdjacencyMatrix[gg]]

??DimensionOfGenerator

DimensionOfGenerator[gg]

DisplayBigraph[SymmetricBigraphs[4][[6]]]

DisplayBigraph/@SymmetricBigraphs[5]

DisplayBigraph[GradedBigraph[m,6]]