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{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}
In[]:=
GraphAutomorphismGroup[Rule@@@{{x,y},{x,z}}]
Out[]=
PermutationGroup[{Cycles[{{2,3}}]}]
In[]:=
Partition[Range[10],2]
Out[]=
{{1,2},{3,4},{5,6},{7,8},{9,10}}
In[]:=
WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Partition[Range[10],2],3,"FinalState"]
Out[]=
{{1,2},{3,4},{5,6},{7,8},{9,10}}
In[]:=
EnumerateHypergraphs[{{2,2}}]
Out[]=
{{{1,1},{1,1}},{{1,1},{1,2}},{{1,1},{2,1}},{{1,2},{1,2}},{{1,2},{2,1}},{{1,2},{1,3}},{{1,2},{2,3}},{{1,2},{3,2}}}
What node interchanges can we do that produce isomorphic results results after n steps?
{{1,2},{1,3},{4,5},{4,6}}
In a single hypergraph
In[]:=
EnumerateHypergraphs[{{2,3}}]
Out[]=
{{1,2,2},{1,3,2}}
FindCanonicalHypergraph[]
In[]:=
GraphData["TetrahedralGraph"]
Out[]=
In[]:=
EdgeList
Out[]=
{12,13,14,23,24,34}
In[]:=
GraphAutomorphismGroup
Out[]=
PermutationGroup[{Cycles[{{3,4}}],Cycles[{{2,3}}],Cycles[{{1,2}}]}]
In[]:=
{12,13,14,23,24,34}/.{12,21}
Out[]=
{21,23,24,13,14,34}
In[]:=
Graph[%]
Out[]=
In[]:=
RandomGraph[{5,8}]
Out[]=
In[]:=
EdgeList[%]
Out[]=
{12,15,23,24,25,34,35,45}
In[]:=
Graph[%/.{41,14}]
Out[]=
Given a hypergraph, permute the labels, and see when it is the same
Given a hypergraph, permute the labels, and see when it is the same