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Hypergraph

Guides

  • Hypergraph Functionality

Tech Notes

  • Hypergraph Rewriting

Symbols

  • AdjacencyHypergraph
  • AdjacencyTensor
  • CanonicalHypergraph
  • CanonicalHypergraphRule
  • ConnectedHypergraphQ
  • CyclicEdge
  • EdgeListTagged
  • EdgeMultiplicity
  • EdgeSymmetry
  • EnumerateHypergraphRules
  • EnumerateHypergraphs
  • EnumerateOrderedHypergraphs
  • EnumerateWolframModelRules
  • HighlightRule
  • HyperedgeList
  • Hyperedge
  • Hyperedges
  • HyperedgesQ
  • Hypergraph3D
  • HypergraphArityReduce
  • HypergraphDraw
  • HypergraphEmbedding
  • HypergraphHadamardProduct
  • HypergraphIncidenceMatrix
  • HypergraphIncidence
  • HypergraphInsertionBracketDegree
  • HypergraphInsertionBracket
  • HypergraphInsertion
  • HypergraphLargeQ
  • Hypergraph
  • HypergraphQ
  • HypergraphRuleDraw
  • HypergraphRule
  • HypergraphRuleQ
  • HypergraphToGraph
  • HypergraphTransitionMatrix
  • HypergraphUnion
  • HypermatrixGraph
  • Hypermatrix
  • HypermatrixQ
  • IncidenceHypergraph
  • IsomorphicHypergraphQ
  • KoszulSign
  • LinkedHypergraph
  • OrderedHypergraphToGraph
  • RandomAllHypergraph
  • RandomConnectedHypergraph
  • RandomHypergraph
  • RandomHypergraphRule
  • SetHypergraphSummaryThresholds
  • SimpleHypergraph
  • SimpleHypergraphPlot3D
  • SimpleHypergraphPlot
  • SimpleHypergraphQ
  • ToLabeledEdges
  • ToLabeledPatternEdges
  • ToOrderedHypergraph
  • ToPatternRules
WolframInstitute`Hypergraph`
RandomAllHypergraph
​
RandomAllHypergraph
[{n,{{
m
1
,
a
1
},{
m
2
,
a
2
},…}}]
gives a pseudorandom hypergraph on n atoms with
𝑚
1
hyperedges of arity
𝑎
1
,
𝑚
2
hyperedges of arity
𝑎
2
, etc, with every hyperedge slot drawn independently and uniformly.
​
​
RandomAllHypergraph
[{
Automatic
,{{
m
1
,
a
1
},…}}]
picks n uniformly at random between 1 and the total number of vertex slots the signature requests.
​
Details and Options
▪
Unlike
RandomHypergraph
, the atom count and the signature are bundled into a single list argument
{n,sig}
, and
RandomAllHypergraph
takes no options: there is no
"Simple"
or
"Connected"
option, and no
Hypergraph
options are applied to the result.
▪
Each hyperedge slot is filled independently and uniformly from 1 through n, with no rejection sampling: the result can contain repeated vertices within a hyperedge, duplicate hyperedges, and can be disconnected.
▪
The result is
Hypergraph[Range[n],edges]
: all n vertices stay in the vertex list even if some never appear in an edge, unlike
RandomHypergraph
which drops unused atoms.
▪
With
Automatic
, n is a random integer between 1 and
Total[Times@@@sig]
, the total number of vertex slots the signature requests.
▪
Use
SeedRandom
to get a reproducible result.
​
Examples  
(6)
Basic Examples  
(1)
Generate a pseudorandom hypergraph on five atoms with three binary hyperedges:
In[1]:=
SeedRandom[1];
RandomAllHypergraph
[{5,{{3,2}}}]
Out[1]=
Hypergraph
Vertices: 5
Edges: 3

Scope  
(1)

Properties & Relations  
(3)

Possible Issues  
(1)

SeeAlso
RandomHypergraph
 
▪
RandomConnectedHypergraph
 
▪
Hypergraph
RelatedGuides
▪
HypergraphFunctionality
""

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