Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
TensorNetworkRemoveCycles  |
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Examples
(5)
Scope
(3)
Unannotated directed graph
(1)
Unannotated directed graph. A raw cyclic Graph gets cup/cap vertices and untagged DirectedEdges:
In[1]:=
gU=Graph[{12,23,31}];
In[2]:=
EdgeList
[gU]
 | TensorNetworkRemoveCycles |
The new vertices carry the labels "Cup" and "Cap":
In[3]:=
AnnotationValue
[gU],VertexList
[gU],VertexLabels
 | TensorNetworkRemoveCycles |
 | TensorNetworkRemoveCycles |
Annotated TN graph
(1)
Multi-cycle graph
(1)
Applications
(1)
Properties & Relations
(1)
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A simple directed 3-cycle is broken by inserting one cup/cap pair:
In[1]:=
g=Graph[{12,23,31}];
In[2]:=
 | TensorNetworkRemoveCycles |
The result is acyclic:
In[3]:=
AcyclicGraphQ
[g]
| TensorNetworkRemoveCycles |
Each cycle adds two vertices (a cup and a cap) to the input:
In[4]:=
VertexCount[g],VertexCount
[g]
 | TensorNetworkRemoveCycles |
The cup and cap carry a flattened identity matrix as their tensor:
In[5]:=
res=
[g];
 | TensorNetworkRemoveCycles |
In[6]:=
AnnotationValue[{res,VertexList[res]},VertexLabels]
""