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WOLFRAM NOTEBOOK
In[]:=
Apply[UndirectedEdge,(WolframModel[{{0,1},{2,1}}{{0,2}},#,"FinalState"]&)/@WolframModel[{{0,1},{0,2},{0,3}}{{4,5},{6,5},{4,7},{8,7},{6,9},{8,9},{4,1},{6,2},{8,3}},{{0,1},{2,1},{0,3},{4,3},{0,5},{6,5},{2,7},{4,7},{2,8},{6,8},{4,9},{6,9}},4,"StatesList"],{2}]
Out[]=
In[]:=
Graph/@%
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In[]:=
siers=Take[%131,4]
Out[]=
In[]:=
Gather[(Function[v,NeighborhoodGraph[#,v,1]]/@VertexList[#]),IsomorphicGraphQ]&/@siers;
In[]:=
Map[Length,%,{2}]
Out[]=
{{4},{12},{36},{108}}
In[]:=
Gather[(Function[v,NeighborhoodGraph[#,v,2]]/@VertexList[#]),IsomorphicGraphQ]&/@siers;
In[]:=
Map[Length,%,{2}]
Out[]=
{{4},{12},{36},{108}}
In[]:=
Gather[(Function[v,NeighborhoodGraph[#,v,3]]/@VertexList[#]),IsomorphicGraphQ]&/@siers;
In[]:=
Map[Length,%,{2}]
Out[]=
{{4},{12},{24,12},{72,36}}
In[]:=
Map[Length,Gather[(Function[v,NeighborhoodGraph[#,v,4]]/@VertexList[#]),IsomorphicGraphQ]]&/@siers
Out[]=
{{4},{12},{24,12},{72,36}}
In[]:=
Map[Length,Gather[(Function[v,NeighborhoodGraph[#,v,4]]/@VertexList[#]),IsomorphicGraphQ]]&/@%131
Out[]=
{{4},{12},{24,12},{72,36},{216,108}}
In[]:=
Map[Length,Gather[(Function[v,NeighborhoodGraph[#,v,5]]/@VertexList[#]),IsomorphicGraphQ]]&/@%131
Out[]=
{{4},{12},{24,12},{72,36},{216,108}}
Map[Length,%,{2}]
TableWithgr=
,ReverseSortBy[(Graph[CanonicalGraph[First[#]],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize40]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,r]&/@VertexList[gr],IsomorphicGraphQ],Last],{r,4}
In[]:=
TableWithgr=
,ReverseSortBy[(Graph[CanonicalGraph[First[#]],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize40]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,r]&/@VertexList[gr],IsomorphicGraphQ],Last],{r,4}
Out[]=
In[]:=
TableWithgr=
,ReverseSortBy[(Graph[CanonicalGraph[First[#]],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize40]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,r]&/@VertexList[gr],IsomorphicGraphQ],Last],{r,20}
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In[]:=
Length/@%
Out[]=
{1,1,2,2,2,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1}
In[]:=
TableWithgr=
,ReverseSortBy[(Graph[CanonicalGraph[First[#]],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize40]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,r]&/@VertexList[gr],IsomorphicGraphQ],Last],{r,4}
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In[]:=
CountsValuesGraphNeighborhoodVolumes
Out[]=
{1,4,8,13,18,26,33,40,46,56,66,80,90,102,108}24,{1,4,8,13,18,26,34,41,48,58,70,80,89,100,105,108}24,{1,4,8,14,20,26,33,41,48,56,66,82,93,100,105,108}24,{1,4,8,13,18,26,34,43,50,62,70,80,89,98,105,108}24,{1,4,8,14,20,26,34,46,56,62,70,82,92,98,104,108}12
KaryTree[
Apply[UndirectedEdge,(WolframModel[{{0,1},{2,1}}{{0,2}},#,"FinalState"]&)/@WolframModel[{{0,1},{0,2},{0,3}}{{4,5},{6,5},{4,7},{8,7},{6,9},{8,9},{4,1},{6,2},{8,3}},{{0,1},{2,1},{0,3},{4,3},{0,5},{6,5},{2,7},{4,7},{2,8},{6,8},{4,9},{6,9}},4,"StatesList"],{2}]
In[]:=
GraphData["TetrahedralGraph"]
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Ordinary Sierpinski
Ordinary Sierpinski
Cayley graph
Cayley graph
Random Cayley Graph
Random Cayley Graph
Heisenberg Group
Heisenberg Group