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Hypergraph

Guides

  • Hypergraph Functionality

Symbols

  • InsertionBracket
  • AdjacencyHypergraph
  • AdjacencyTensor
  • EnumerateHypergraphs
  • HighlightRule
  • HypergraphDraw
  • HypergraphIncidenceMatrix
  • Hypergraph
  • HypergraphRule
  • HypermatrixGraph
  • Hypermatrix
  • IncidenceHypergraph
  • HypegraphInsertionBracket
  • SimpleHypergraphPlot
WolframInstitute`HypergraphLoader`
HypegraphInsertionBracket
​
HypergraphInsertionBracket
[
hypegraph
1
,
hypegraph
2
,...]
computes the insertion bracket of given hypergraphs with graded vertices
​
​
HypergraphInsertionBracket
[
hypergraph
1

a
11
,...,
hypergraph
2

a
21
,...,...]
distributes the insertion bracket linearly in each input
​
Details
​
Examples  
(4)
Basic Examples  
(3)
Compute the graded insertion Lie bracket of two graded hypergraphs:
In[1]:=
HypergraphInsertionBracket

Hypergraph
[{1,2,3},{{1,2,3}},"VertexAnnotationRules"{"Degree"{10,20,31}}],
Hypergraph
[{1,2},{{1,2}},"VertexAnnotationRules"{"Degree"{10,21}}]//​​KeyMap
Hypergraph
[#,VertexLabelsAutomatic,VertexStyle(Lookup[Lookup[AbsoluteOptions[#],"VertexAnnotationRules"],"Degree"]/.(v_deg_)(vIf[OddQ[deg],Red,Blue]))]&
Out[1]=

-1,
-1,
-1
​
Compute the insertion Lie bracket of two rooted hypergraphs:
In[1]:=
HypergraphInsertionBracket

Hypergraph
[{1,2,3},{{1,2,3}}],
Hypergraph
[{1,2},{{1,2}}],"Kind""Rooted"//KeyMap
Hypergraph
[#,VertexStyle{First[VertexList[#]]Red}]&
Out[1]=

2,
-1
​
Compute the insertion Lie bracket of two tagged hypergraphs with cyclic edge symmetry:
In[1]:=
HypergraphInsertionBracket

Hypergraph
[{{1,4},{1,2,3},{4,5,6}},"EdgeSymmetry""Cyclic"],
Hypergraph
[{{1,2,3},{1,2}},"EdgeSymmetry""Cyclic"],"Kind""Tagged"//KeyMap
Hypergraph
[#,EdgeStyle{First[EdgeList[#]]Red}]&
Out[1]=

2,
2,
2,
-2
Properties & Relations  
(1)

RelatedLinks
▪
M. Marcolli, A. Port: Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory (2015)
P. Hajek: [WWS25] Lie brackets on hypergraphs (2025)
P. Hajek: Insertion bracket for Wolfram hypergraphs (to appear)
""

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