FoldList[PNShakeGraph[PNEvolve[{rl},#1,#2],s]&,PNTetra,tl]
{NodeToTriangleRule,4*3^Range[0,steps-2],300}
VertexReplace
In[]:=
GraphData["TetrahedralGraph"]
Out[]=
In[]:=
TrivalentGraph[list_]:=UndirectedGraph[Rule@@@DeleteDuplicates[Sort/@Catenate[{#[[{1,2}]],#[[{2,3}]],#[[{3,1}]]}&/@list]]]
In[]:=
TrivalentGraph/@NestList[Catenate[Replace[#,{x_,y_,z_}Module[{a,b,c},{{x,b,c},{a,y,c},{b,z,a}}]]&/@#]&,{{1,2,3},{1,2,4},{1,3,4},{2,3,4}},3]
Out[]=

Attempt 0

In[]:=
SimpleGraph[Flatten[Thread/@#]]&/@NestList[Flatten[#/.(x_<->{a_,b_,c_}):>Module[{ap,bp,cp},{ap{a,bp,cp},bp{ap,b,cp},cp{ap,bp,c}}]]&,{1{2,3,4},2{1,3,4},3{1,2,4},4{1,2,3}},3]
Out[]=
In[]:=
NeighborhoodGraph
,#,1&/@VertexList

Out[]=
OSZAR »