Ordinary graphs
Ordinary graphs
Orderlessness
Orderlessness
In[]:=
unorderedHyperedgesToGraph[edges_]:=Catenate[Replace[edges,vertices_Thread[Unique[]vertices],{1}]]
In[]:=
unorderedHyperedgesToGraph[{{1,2,3},{3,1,2},{3,1,1}}]
Out[]=
{$104631,$104632,$104633,$104643,$104641,$104642,$104653,$104651,$104651}
In[]:=
Graph[%]
Out[]=
Maps vertices representing edges to vertices representing vertices... . [[[ This is basically a picture of the mapping from edges to vertices ]]]
Unordered hypergraph is just like this mapping
Two-Way Rules
Two-Way Rules
Doesn’t always make sense to have 2-way ( vs. AB -> BA, BA -> AB )
Everything is defined by structure
{{x,y}{y,x}}
Two-Way Rules
Two-Way Rules
In[]:=
EnumerateWolframModelRules[{{1,2}}{{1,2}}]
Out[]=
In[]:=
Select[EnumerateWolframModelRules[{{1,2}}{{1,2}}],FindCanonicalWolframModel[Reverse[#]]=!=#&]
Out[]=
{{{1,1}}{{1,2}},{{1,1}}{{2,1}},{{1,2}}{{1,1}},{{1,2}}{{2,2}},{{1,2}}{{2,3}},{{1,2}}{{3,1}}}
In[]:=
EnumerateWolframModelRules[{{2,2}}{{2,2}}]
Out[]=
In[]:=
ParallelMapMonitored[WolframModel[{Reverse[#],#},{{0,0}},5]["FinalStatePlot",ImageSizeTiny]&,EnumerateWolframModelRules[{{2,2}}{{1,2}}]]
Out[]=
May or may not use the reversed rule
In[]:=
Select[EnumerateWolframModelRules[{{2,2}}{{1,2}}],FindCanonicalWolframModel[Reverse[#]]=!=#&]
Out[]=
Relationship to e.g. Cayley Graph
Relationship to e.g. Cayley Graph
Symbolic Representation of Something Else?
Symbolic Representation of Something Else?
E.g. relations for a Lie algebra
E.g. axiom systems for anything