In[]:=
Graph[MultiwaySystem[WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}],{{{0,0},{0,0}}},2,"StatesGraph"],VertexSize1]
Out[]=
In[]:=
Graph[MultiwaySystem[WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}],{{{0,0},{0,0}}},2,"BranchialGraph"],VertexSize1]
Out[]=
In[]:=
Graph[MultiwaySystem[WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}],{{{0,0},{0,0}}},3,"BranchialGraph"],VertexSize1]
Out[]=
In[]:=
TransitiveReductionGraph[%]
Out[]=
{{x,y},{x,z}}{{y,z},{y,w},{z,w},{x,w}}