diff --git a/Project.toml b/Project.toml
index 69fe3c7d..3f5cd526 100644
--- a/Project.toml
+++ b/Project.toml
@@ -29,6 +29,7 @@ SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
+TupleTools = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
 
 [compat]
 AbstractTrees = "0.4.4"
@@ -54,6 +55,7 @@ SplitApplyCombine = "1.2"
 StaticArrays = "1.5.12"
 Suppressor = "0.2"
 TimerOutputs = "0.5.22"
+TupleTools = "1.4"
 julia = "1.7"
 
 [extras]
diff --git a/README.md b/README.md
index 872711a6..7c13ee59 100644
--- a/README.md
+++ b/README.md
@@ -36,18 +36,18 @@ and 3 edge(s):
 3 => 4
 
 with vertex data:
-4-element Dictionaries.Dictionary{Int64, Any}
- 1 │ ((dim=2|id=739|"1↔2"),)
- 2 │ ((dim=2|id=739|"1↔2"), (dim=2|id=920|"2↔3"))
- 3 │ ((dim=2|id=920|"2↔3"), (dim=2|id=761|"3↔4"))
- 4 │ ((dim=2|id=761|"3↔4"),)
+4-element Dictionary{Int64, Any}
+ 1 │ ((dim=2|id=739|"1,2"),)
+ 2 │ ((dim=2|id=739|"1,2"), (dim=2|id=920|"2,3"))
+ 3 │ ((dim=2|id=920|"2,3"), (dim=2|id=761|"3,4"))
+ 4 │ ((dim=2|id=761|"3,4"),)
 
 julia> tn[1]
-ITensor ord=1 (dim=2|id=739|"1↔2")
+ITensor ord=1 (dim=2|id=739|"1,2")
 NDTensors.EmptyStorage{NDTensors.EmptyNumber, NDTensors.Dense{NDTensors.EmptyNumber, Vector{NDTensors.EmptyNumber}}}
 
 julia> tn[2]
-ITensor ord=2 (dim=2|id=739|"1↔2") (dim=2|id=920|"2↔3")
+ITensor ord=2 (dim=2|id=739|"1,2") (dim=2|id=920|"2,3")
 NDTensors.EmptyStorage{NDTensors.EmptyNumber, NDTensors.Dense{NDTensors.EmptyNumber, Vector{NDTensors.EmptyNumber}}}
 
 julia> neighbors(tn, 1)
@@ -88,14 +88,14 @@ and 4 edge(s):
 (1, 2) => (2, 2)
 
 with vertex data:
-4-element Dictionaries.Dictionary{Tuple{Int64, Int64}, Any}
- (1, 1) │ ((dim=2|id=74|"1×1↔2×1"), (dim=2|id=723|"1×1↔1×2"))
- (2, 1) │ ((dim=2|id=74|"1×1↔2×1"), (dim=2|id=823|"2×1↔2×2"))
- (1, 2) │ ((dim=2|id=723|"1×1↔1×2"), (dim=2|id=712|"1×2↔2×2"))
- (2, 2) │ ((dim=2|id=823|"2×1↔2×2"), (dim=2|id=712|"1×2↔2×2"))
+4-element Dictionary{Tuple{Int64, Int64}, Any}
+ (1, 1) │ ((dim=2|id=74|"1×1,2×1"), (dim=2|id=723|"1×1,1×2"))
+ (2, 1) │ ((dim=2|id=74|"1×1,2×1"), (dim=2|id=823|"2×1,2×2"))
+ (1, 2) │ ((dim=2|id=723|"1×1,1×2"), (dim=2|id=712|"1×2,2×2"))
+ (2, 2) │ ((dim=2|id=823|"2×1,2×2"), (dim=2|id=712|"1×2,2×2"))
 
 julia> tn[1, 1]
-ITensor ord=2 (dim=2|id=74|"1×1↔2×1") (dim=2|id=723|"1×1↔1×2")
+ITensor ord=2 (dim=2|id=74|"1×1,2×1") (dim=2|id=723|"1×1,1×2")
 NDTensors.EmptyStorage{NDTensors.EmptyNumber, NDTensors.Dense{NDTensors.EmptyNumber, Vector{NDTensors.EmptyNumber}}}
 
 julia> neighbors(tn, (1, 1))
@@ -118,9 +118,9 @@ and 1 edge(s):
 (1, 1) => (1, 2)
 
 with vertex data:
-2-element Dictionaries.Dictionary{Tuple{Int64, Int64}, Any}
- (1, 1) │ ((dim=2|id=74|"1×1↔2×1"), (dim=2|id=723|"1×1↔1×2"))
- (1, 2) │ ((dim=2|id=723|"1×1↔1×2"), (dim=2|id=712|"1×2↔2×2"))
+2-element Dictionary{Tuple{Int64, Int64}, Any}
+ (1, 1) │ ((dim=2|id=74|"1×1,2×1"), (dim=2|id=723|"1×1,1×2"))
+ (1, 2) │ ((dim=2|id=723|"1×1,1×2"), (dim=2|id=712|"1×2,2×2"))
 
 julia> tn_2 = subgraph(v -> v[1] == 2, tn)
 ITensorNetwork{Tuple{Int64, Int64}} with 2 vertices:
@@ -132,9 +132,9 @@ and 1 edge(s):
 (2, 1) => (2, 2)
 
 with vertex data:
-2-element Dictionaries.Dictionary{Tuple{Int64, Int64}, Any}
- (2, 1) │ ((dim=2|id=74|"1×1↔2×1"), (dim=2|id=823|"2×1↔2×2"))
- (2, 2) │ ((dim=2|id=823|"2×1↔2×2"), (dim=2|id=712|"1×2↔2×2"))
+2-element Dictionary{Tuple{Int64, Int64}, Any}
+ (2, 1) │ ((dim=2|id=74|"1×1,2×1"), (dim=2|id=823|"2×1,2×2"))
+ (2, 2) │ ((dim=2|id=823|"2×1,2×2"), (dim=2|id=712|"1×2,2×2"))
 ```
 
 
@@ -155,13 +155,13 @@ and 2 edge(s):
 2 => 3
 
 with vertex data:
-3-element Dictionaries.Dictionary{Int64, Vector{Index}}
+3-element Dictionary{Int64, Vector{Index}}
  1 │ Index[(dim=2|id=598|"S=1/2,Site,n=1")]
  2 │ Index[(dim=2|id=457|"S=1/2,Site,n=2")]
  3 │ Index[(dim=2|id=683|"S=1/2,Site,n=3")]
 
 and edge data:
-0-element Dictionaries.Dictionary{NamedEdge{Int64}, Vector{Index}}
+0-element Dictionary{NamedEdge{Int64}, Vector{Index}}
 
 julia> tn1 = ITensorNetwork(s; link_space=2)
 ITensorNetwork{Int64} with 3 vertices:
@@ -175,10 +175,10 @@ and 2 edge(s):
 2 => 3
 
 with vertex data:
-3-element Dictionaries.Dictionary{Int64, Any}
- 1 │ ((dim=2|id=598|"S=1/2,Site,n=1"), (dim=2|id=123|"1↔2"))
- 2 │ ((dim=2|id=457|"S=1/2,Site,n=2"), (dim=2|id=123|"1↔2"), (dim=2|id=656|"2↔3…
- 3 │ ((dim=2|id=683|"S=1/2,Site,n=3"), (dim=2|id=656|"2↔3"))
+3-element Dictionary{Int64, Any}
+ 1 │ ((dim=2|id=598|"S=1/2,Site,n=1"), (dim=2|id=123|"1,2"))
+ 2 │ ((dim=2|id=457|"S=1/2,Site,n=2"), (dim=2|id=123|"1,2"), (dim=2|id=656|"2,3…
+ 3 │ ((dim=2|id=683|"S=1/2,Site,n=3"), (dim=2|id=656|"2,3"))
 
 julia> tn2 = ITensorNetwork(s; link_space=2)
 ITensorNetwork{Int64} with 3 vertices:
@@ -192,10 +192,10 @@ and 2 edge(s):
 2 => 3
 
 with vertex data:
-3-element Dictionaries.Dictionary{Int64, Any}
- 1 │ ((dim=2|id=598|"S=1/2,Site,n=1"), (dim=2|id=382|"1↔2"))
- 2 │ ((dim=2|id=457|"S=1/2,Site,n=2"), (dim=2|id=382|"1↔2"), (dim=2|id=190|"2↔3…
- 3 │ ((dim=2|id=683|"S=1/2,Site,n=3"), (dim=2|id=190|"2↔3"))
+3-element Dictionary{Int64, Any}
+ 1 │ ((dim=2|id=598|"S=1/2,Site,n=1"), (dim=2|id=382|"1,2"))
+ 2 │ ((dim=2|id=457|"S=1/2,Site,n=2"), (dim=2|id=382|"1,2"), (dim=2|id=190|"2,3…
+ 3 │ ((dim=2|id=683|"S=1/2,Site,n=3"), (dim=2|id=190|"2,3"))
 
 julia> @visualize tn1;
     ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 
diff --git a/src/treetensornetworks/abstracttreetensornetwork.jl b/src/treetensornetworks/abstracttreetensornetwork.jl
index 0bb6668a..72642687 100644
--- a/src/treetensornetworks/abstracttreetensornetwork.jl
+++ b/src/treetensornetworks/abstracttreetensornetwork.jl
@@ -1,3 +1,5 @@
+using TupleTools: TupleTools
+
 abstract type AbstractTreeTensorNetwork{V} <: AbstractITensorNetwork{V} end
 
 const AbstractTTN = AbstractTreeTensorNetwork
@@ -334,7 +336,7 @@ function permute(ψ::AbstractTTN, ::Tuple{typeof(linkind),typeof(siteinds),typeo
   ψ̃ = copy(ψ)
   for v in vertices(ψ)
     ls = [only(linkinds(ψ, n => v)) for n in neighbors(ψ, v)] # TODO: won't work for multiple indices per link...
-    ss = sort(Tuple(siteinds(ψ, v)); by=plev)
+    ss = TupleTools.sort(Tuple(siteinds(ψ, v)); by=plev)
     setindex_preserve_graph!(
       ψ̃, permute(ψ[v], filter(!isnothing, (ls[1], ss..., ls[2:end]...))), v
     )
diff --git a/test/Project.toml b/test/Project.toml
index 0d48cce5..ac355cb3 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -7,6 +7,7 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Glob = "c27321d9-0574-5035-807b-f59d2c89b15c"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 GraphsFlows = "06909019-6f44-4949-96fc-b9d9aaa02889"
+ITensorNetworks = "2919e153-833c-4bdc-8836-1ea460a35fc7"
 ITensorUnicodePlots = "73163f41-4a9e-479f-8353-73bf94dbd758"
 ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
 KaHyPar = "2a6221f6-aa48-11e9-3542-2d9e0ef01880"