Wolfram/TensorNetworks | Paclet Repository

Wolfram`TensorNetworks`

TensorNetworkIndexGraph

TensorNetworkIndexGraph [graph]
	returns a Graph whose vertices are the individual indices of the tensor-network graph graph and whose edges encode both contractions between tensors and co-occurrence of indices within each tensor.

Details and Options

▪

The input

graph

must be an annotated tensor-network graph satisfying

TensorNetworkGraphQ

. Build one with

ToTensorNetworkGraph

or read it from a

TensorNetwork

object via the

"Graph"

property. The diagnostic check

TensorNetworkGraphQ

[True]

(verbose mode) is used, so invalid inputs leave the expression unevaluated and print messages.

▪

Vertices of the returned graph are individual indices (each a

Superscript

Subscript

labeled by its parent tensor's vertex id), so the vertex set is

Catenate

[

TensorNetworkIndices

[graph]]

▪

Edges come in two kinds:

▪

• Contraction edges: one directed edge per inter-tensor index contraction, obtained from

EdgeTags

[graph]

. Each tag is a pair

{srcIndex,tgtIndex}

and becomes the directed edge

srcIndextgtIndex

▪

• Co-occurrence edges: for each tensor vertex of

graph

, every pair of indices on that tensor is connected by an undirected edge. Equivalently, each tensor contributes a complete subgraph over its own index list.

▪

Additional

Graph

options are forwarded to the returned graph, and

VertexLabels



Automatic

is supplied by default so each vertex is labeled with its index.

▪

The index graph is complementary to

ToTensorNetworkGraph

: in the tensor-network graph, vertices are tensors and edges are contracted indices; in the index graph, vertices are indices and edges record both contractions between tensors and co-occurrence within a tensor.

Examples

(6)

Basic Examples

(1)

Build an annotated tensor-network graph from a small TensorNetwork:

In[1]:=

tn=