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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`
HypergraphInsertionBracketDegree
​
HypergraphInsertionBracketDegree
[hg]
gives the grading degree of the hypergraph hg used by
HypergraphInsertionBracket
.
​
Details and Options
▪
The degree is
ℎ𝑔=deg(ℎ𝑔)-deg(root)
: the sum of the vertex degrees of hg, minus the degree of its root vertex, which by convention is the first vertex in
VertexList
[hg].
▪
Vertex degrees are read from the
"Degree"
vertex annotation, set with the option
"VertexAnnotationRules"{"Degree"{vd,…}}
; a vertex with no explicit degree defaults to 0.
▪
HypergraphInsertionBracket
uses this degree, together with the
KoszulSign
convention, to sign the terms of its
"Ordered"
and
"Rooted"
insertion brackets, and to restrict insertion to vertices of matching degree.
▪
HypergraphInsertionBracketDegree
takes no options.
​
Examples  
(4)
Basic Examples  
(2)
A hypergraph with no
"Degree"
annotation has degree 0:
In[1]:=
HypergraphInsertionBracketDegree

Hypergraph
[{{1,2,3}}]
Out[1]=
0
_________________________________________________________________________________________________________________
A hypergraph made only of isolated vertices also has degree 0:
In[1]:=
HypergraphInsertionBracketDegree

Hypergraph
[{1,2},{}]
Out[1]=
0
Scope  
(1)

Possible Issues  
(1)

SeeAlso
HypergraphInsertionBracket
 
▪
Hypergraph
RelatedGuides
▪
HypergraphFunctionality
""

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