Remove approximate-contract (density_matrix / ttn_svd) algorithms (#329)

## Summary

Delete the entire `src/contract_approx/` module (8 files, ~1200 lines)
and the dead `ITensorNetworksGraphsFlowsExt` extension that only served
it.

**Breaking:**
- `contract(tn; alg = "density_matrix")` and `contract(tn; alg =
"ttn_svd")` are removed.
- The `contract_approx` function and all of its supporting machinery
(`path_graph_structure`, `binary_tree_structure`, `_partition`,
`_mincut_partitions`, `_contract_deltas`, `_rem_leaf_vertices!`, …) are
gone.
- `GraphsFlows` is no longer a weak-dep / extension trigger of
`ITensorNetworks`. It remains a direct test-time dep for the graph
mincut test in `test/test_itensornetwork.jl`.

**What stays:**
- `contract(tn; alg = "exact")` and the rest of the contraction pipeline
(TensorOperations / OMEinsumContractionOrders extensions) are
unaffected.

**Incidental import cleanups**

A few imports were previously available inside `ITensorNetworks` as a
side effect of `using` clauses in `src/contract_approx/*.jl`. They are
now imported directly by the files that actually use them:
- `Graphs: rem_vertex!` —
`src/treetensornetworks/opsum_to_ttn/opsum_to_ttn.jl`
- `ITensors: inds` — `src/abstractitensornetwork.jl`
- `ITensors: noncommoninds` — `src/apply.jl`
- `NamedGraphs.GraphsExtensions: disjoint_union` —
`src/formnetworks/linearformnetwork.jl`,
`src/formnetworks/bilinearformnetwork.jl`

**Version**

Bumps to `0.17.0` (pre-1.0 minor bump = breaking) and updates pinned
`ITensorNetworks` compat in `test/`, `docs/`, and `examples/`
Project.toml.

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: mtfishman

Project.toml

@@ -1,6 +1,6 @@
 name = "ITensorNetworks"
 uuid = "2919e153-833c-4bdc-8836-1ea460a35fc7"
-version = "0.16.0"
+version = "0.17.0"
 authors = ["Matthew Fishman <mfishman@flatironinstitute.org>, Joseph Tindall <jtindall@flatironinstitute.org> and contributors"]
 
 [workspace]
@@ -39,13 +39,11 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 TupleTools = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
 
 [weakdeps]
-GraphsFlows = "06909019-6f44-4949-96fc-b9d9aaa02889"
 OMEinsumContractionOrders = "6f22d1fd-8eed-4bb7-9776-e7d684900715"
 Observers = "338f10d5-c7f1-4033-a7d1-f9dec39bcaa0"
 TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
 
 [extensions]
-ITensorNetworksGraphsFlowsExt = "GraphsFlows"
 ITensorNetworksOMEinsumContractionOrdersExt = "OMEinsumContractionOrders"
 ITensorNetworksObserversExt = "Observers"
 ITensorNetworksTensorOperationsExt = "TensorOperations"
@@ -63,7 +61,6 @@ Dictionaries = "0.4"
 Distributions = "0.25.86"
 DocStringExtensions = "0.9"
 Graphs = "1.8"
-GraphsFlows = "0.1.1"
 ITensors = "0.7, 0.8, 0.9"
 IsApprox = "0.1, 1, 2"
 IterTools = "1.4"

docs/Project.toml

@@ -16,7 +16,7 @@ path = ".."
 Documenter = "1.10"
 Graphs = "1"
 ITensorFormatter = "0.2.27"
-ITensorNetworks = "0.16"
+ITensorNetworks = "0.17"
 ITensors = "0.9"
 Literate = "2.20.1"
 NamedGraphs = "0.8.2"

examples/Project.toml

@@ -5,4 +5,4 @@ ITensorNetworks = "2919e153-833c-4bdc-8836-1ea460a35fc7"
 path = ".."
 
 [compat]
-ITensorNetworks = "0.16"
+ITensorNetworks = "0.17"

ext/ITensorNetworksGraphsFlowsExt/ITensorNetworksGraphsFlowsExt.jl

@@ -13,14 +13,6 @@ include("abstractitensornetwork.jl")
 include("contraction_sequences.jl")
 include("tebd.jl")
 include("itensornetwork.jl")
-include("contract_approx/mincut.jl")
-include("contract_approx/contract_deltas.jl")
-include("contract_approx/utils.jl")
-include("contract_approx/density_matrix.jl")
-include("contract_approx/ttn_svd.jl")
-include("contract_approx/contract_approx.jl")
-include("contract_approx/partition.jl")
-include("contract_approx/binary_tree_partition.jl")
 include("contract.jl")
 include("specialitensornetworks.jl")
 include("partitioneditensornetwork.jl")

src/ITensorNetworks.jl

@@ -6,7 +6,7 @@ using Dictionaries: Dictionary
 using Graphs: Graphs, Graph, add_edge!, add_vertex!, bfs_tree, center, dst, edges, edgetype,
     ne, neighbors, rem_edge!, src, vertices
 using ITensors: ITensors, @Algorithm_str, ITensor, addtags, combiner, commoninds,
-    commontags, contract, dag, hascommoninds, noprime, onehot, prime, replaceprime,
+    commontags, contract, dag, hascommoninds, inds, noprime, onehot, prime, replaceprime,
     replacetags, setprime, settags, sim, swaptags, unioninds, uniqueinds
 using LinearAlgebra: LinearAlgebra, factorize
 using MacroTools: @capture

src/abstractitensornetwork.jl

@@ -1,8 +1,8 @@
 using .BaseExtensions: maybe_real
 using Graphs: has_edge
 using ITensors: ITensors, ITensor, Index, Ops, apply, commonind, commoninds, contract, dag,
-    denseblocks, factorize, factorize_svd, hasqns, isdiag, noprime, prime, replaceind,
-    replaceinds, unioninds, uniqueinds
+    denseblocks, factorize, factorize_svd, hasqns, isdiag, noncommoninds, noprime, prime,
+    replaceind, replaceinds, unioninds, uniqueinds
 using KrylovKit: linsolve
 using LinearAlgebra: eigen, norm, qr, svd
 using NamedGraphs: NamedEdge, has_edge

src/apply.jl

@@ -20,15 +20,6 @@ function NDTensors.contract(
     return contract(ts; sequence = sequence_linear_index, kwargs...)
 end
 
-function NDTensors.contract(
-        alg::Union{Algorithm"density_matrix", Algorithm"ttn_svd"},
-        tn::AbstractITensorNetwork;
-        output_structure::Function = path_graph_structure,
-        kwargs...
-    )
-    return contract_approx(alg, tn, output_structure; kwargs...)
-end
-
 function ITensors.scalar(alg::Algorithm"exact", tn::AbstractITensorNetwork; kwargs...)
     return contract(alg, tn; kwargs...)[]
 end