These mathematical objects representing supersymmetric particles, in physics oh my goodness!

AdinkraVertexCoordinates[vertices_, vertexweights_] := Module[
  {coords, ids, coordsList}, 
  coords = Table[{i, j}, {i, -2, 2}, {j, -2, 2}];
  ids = Flatten[Position[vertexweights, #]] & /@ {-4, -3, -2, -1, 1, 
     2, 3, 4};
  coordsList = vertices[[#]] -> coords[[#]] & /@ ids;
  coordsList]
AdinkraGraph[vertices_, vertexweights_, edges_, edgeweights_, 
  colors_] := 
 Graph[Style[vertices[[#]], 
     If[Sign[vertexweights[[#]]] > 0, White, Black]] & /@ 
   Range[Length[vertices]], 
  Style[edges[[#]], colors[edges[[#]][[1]]], Thick] & /@ 
   Range[Length[edges]], VertexWeight -> vertexweights, 
  EdgeWeight -> edgeweights, 
  VertexCoordinates -> 
   AdinkraVertexCoordinates[vertices, vertexweights], 
  DirectedEdges -> False, ImageSize -> Medium]
vertices = {A, B, F, 
   G, \[CapitalPsi]1, \[CapitalPsi]2, \[CapitalPsi]3, \
\[CapitalPsi]4};
vertexweights = {1, 2, 3, 4, -2, -1, -3, -4};
edges = {A -> \[CapitalPsi]2, 
   B -> \[CapitalPsi]4, \[CapitalPsi]3 -> F, \[CapitalPsi]1 -> G, 
   A -> \[CapitalPsi]4, 
   B -> \[CapitalPsi]2, \[CapitalPsi]1 -> F, \[CapitalPsi]3 -> G, 
   A -> \[CapitalPsi]1, 
   B -> \[CapitalPsi]3, \[CapitalPsi]4 -> F, \[CapitalPsi]2 -> G, 
   A -> \[CapitalPsi]3, 
   B -> \[CapitalPsi]1, \[CapitalPsi]2 -> F, \[CapitalPsi]4 -> G};
edgeweights = {2, -1, 4, 3, 4, -3, -2, -1, 1, 2, -3, 2, 3, 4, 1, -2};
colors = <|1 -> Green, 2 -> Purple, 3 -> Orange, 4 -> Red|>;
HorizontalSpacing[n_] := Range[n] - (n + 1)/2;
GraphPlot3D[
 AdinkraGraph[vertices, vertexweights, edges, edgeweights, colors]]

Swapping pairs of original pairings that's the kind of thing it's like word within the word.

AdinkraGraph[vertices_, edges_] := 
 Module[{n = Length[vertices], coordsList}, 
  coordsList = vertices[[#]] -> CirclePoints[n][[#]] & /@ Range[n];
  Graph3D[vertices, edges, 
   VertexStyle -> 
    Table[vertices[[i]] -> Directive[EdgeForm[Black], White], {i, n}],
    VertexCoordinates -> coordsList, ImageSize -> Medium]]
vertices = {A, B, F, 
   G, \[CapitalPsi]1, \[CapitalPsi]2, \[CapitalPsi]3, \
\[CapitalPsi]4};
edges = {A -> \[CapitalPsi]2, 
   B -> \[CapitalPsi]4, \[CapitalPsi]3 -> F, \[CapitalPsi]1 -> G, 
   A -> \[CapitalPsi]4, 
   B -> \[CapitalPsi]2, \[CapitalPsi]1 -> F, \[CapitalPsi]3 -> G, 
   A -> \[CapitalPsi]1, 
   B -> \[CapitalPsi]3, \[CapitalPsi]4 -> F, \[CapitalPsi]2 -> G, 
   A -> \[CapitalPsi]3, 
   B -> \[CapitalPsi]1, \[CapitalPsi]2 -> F, \[CapitalPsi]4 -> G};
GraphPlot3D[AdinkraGraph[vertices, edges]]

I love your visually accurate Adinkra, it's like the number of re-writing operations just isn't enough so you've got these re-writing rules.

LMatricesToAdinkraGraph[L1_, X1_, Y1_, Z1_, bosons_ : {A, B, F, G}, 
  fermions_ : {Subscript[\[CapitalPsi], 1], 
    Subscript[\[CapitalPsi], 2], Subscript[\[CapitalPsi], 3], 
    Subscript[\[CapitalPsi], 4]}, n_ : 2] := 
 Module[{states, vertices, edges}, 
  states = 
   MatrixToAdinkraStates[L1, X1, Y1, bosons, fermions, n][[n + 1]];
  vertices = DeleteDuplicates@Flatten@states;
  edges = Rule @@@ states;
  AdinkraGraph[vertices, edges]]
L1 = {{1, x}, {2, w}, {3, y}, {4, z}};
X1 = {{1, z}, {2, w}, {3, x}, {4, y}};
Y1 = {{1, w}, {2, z}, {3, y}, {4, x}};
Z1 = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}};

GraphPlot3D[LMatricesToAdinkraGraph[L1, X1, Y1, Z1], Boxed -> False, 
 EdgeStyle -> Directive[Thickness[0.005], Opacity[0.5]], 
 VertexSize -> Large, 
 VertexLabelStyle -> Directive[Black, FontSize -> 16], 
 PlotRange -> All, ViewPoint -> {0, -2, 1}]

It's the supersymmetric physics from the set of L-matrices, that generate this visually accurate one and we can make smaller & larger adinkras. We could do the WolframModel rules or a multi-way system setup. I think that this is one of the best things that my eyes have ever seen.