Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
WolframInstitute`Hypergraph`
CyclicEdge  |
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is one of three heads recognizes as edge-symmetry markers in an edge specification: gives symmetry, gives symmetry (the full symmetric group on the edge's vertices), and gives symmetry (the cyclic group generated by rotating the vertex list).
"Ordered"
"Unordered"
"Cyclic"
▪
The cyclic group of a k-ary edge has k elements, the identity and its k - 1 nontrivial rotations; for k = 2 this coincides with symmetry.
"Unordered"
▪
Outside an edge specification, carries no evaluation rules of its own and remains an unevaluated symbolic expression, the same way and do.
▪
reports for a hyperedge specified with ; reconstructs it as a tagged .
"Cyclic"
"Cyclic"
Examples
(5)
Basic Examples
(1)
Build a hypergraph with a cyclic ternary hyperedge:
In[1]:=
hg=
[{1,2,3}]
 | Hypergraph |
 | CyclicEdge |
Out[1]=
Its edge symmetry is reported as :
"Cyclic"
In[2]:=
 | EdgeSymmetry |
Out[2]=
{{Cycles[{}],Cycles[{{1,2,3}}],Cycles[{{1,3,2}}]}}
The full edge symmetry expands into the 3 elements of the cyclic group, the identity and the two nontrivial rotations:
In[3]:=
hg["FullEdgeSymmetry"]
Out[3]=
{{Cycles[{}],Cycles[{{1,2,3}}],Cycles[{{1,3,2}}]}}
Scope
(2)
Properties & Relations
(2)
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