Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
BinaryTensorNetworkQ  |
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A tensor network is binary when every shared index connects exactly two tensors, so the entire network can be contracted by a sequence of pairwise operations. Indices that appear in three or more tensors are called hyperedges and require spider (delta) tensors to be replaced by pairwise contractions before standard path-finders can run.
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The check is : tally the occurrences of every index across all hyperedge lists and confirm none exceeds two.
AllTrue[Counts[Catenate@tn["Hyperedges"]],#≤2&]
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The MPS, TT, MPO, PEPS, TTN, and MERA topologies generated by are binary by construction; a hand-built with three or more tensors sharing the same index is not.
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tn["BinaryQ"]
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converts a network with hyperedges into a binary one by inserting one spider per offending index; on a binary input it is the identity.
SymbolicDeltaProductArray
Examples
(9)
Basic Examples
(3)
A pairwise binary chain has only two-tensor indices, so the predicate is True:
In[1]:=
 | BinaryTensorNetworkQ |
 | TensorNetwork |
Out[1]=
True
When a single index is shared by three tensors, the network has a hyperedge and the predicate is False:
In[1]:=
| BinaryTensorNetworkQ |
| TensorNetwork |
Out[1]=
False
BinaryTensorNetwork inserts a spider tensor for every hyperedge, after which the predicate returns True:
In[1]:=
hyper=
[{{1,2},{1,3},{1,4}}];hyper["BinaryQ"]
 | TensorNetwork |
In[2]:=
| BinaryTensorNetworkQ |
| BinaryTensorNetwork |
Out[2]=
False
Out[2]=
True
Scope
(4)
Properties & Relations
(2)
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