Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
WolframInstitute`Hypergraph`
Hypermatrix  |
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returns a object, which displays as a summary box showing the dimensions of its component arrays; tests for a valid object.
Hypermatrix
HypermatrixQ
Hypermatrix
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Hyperedges are grouped by their arity and edge symmetry: each group of arity- hyperedges becomes a of rank whose dimensions all equal the number of vertices , keyed by the pair of and the symmetry, given as a list of permutations.
𝑘
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Array entries count hyperedge multiplicities, with indices referring to positions in [hg].
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Arity-0 hyperedges are stored as their count instead of an array.
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Unlike , which embeds all hyperedges in a single padded tensor of the maximal rank, a hypermatrix keeps one unpadded array per arity and symmetry.
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In , symmetries is a list of the same length as edges whose elements are lists of generators, one per edge; tagged edges edge -> tag are accepted, with the tag ignored.
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For a hypermatrix hm, gives the list of component arrays, their dimensions, and an association from the arity-symmetry keys to the arrays.
hm["Arrays"]
hm["Dimensions"]
hm["Association"]
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reconstructs a hypergraph from its hypermatrix.
Examples
(7)
Basic Examples
(1)
Compute the hypermatrix of a hypergraph with two binary hyperedges and one ternary hyperedge:
In[1]:=
hm=
[{{1,2},{2,3},{1,2,3}}]
 | Hypermatrix |
 | Hypergraph |
Out[1]=
Hypermatrix
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There is one component array per hyperedge arity:
In[2]:=
hm["Dimensions"]
Out[2]=
{{3,3},{3,3,3}}
In[3]:=
MatrixForm@First@hm["Arrays"]
Out[3]=
0 | 1 | 0 |
0 | 0 | 1 |
0 | 0 | 0 |
Scope
(4)
Properties & Relations
(2)
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