diff --git a/B/BranchFlowModel/Compat.toml b/B/BranchFlowModel/Compat.toml
index 5125e114bb44443..b4d693eaf7bd7f0 100644
--- a/B/BranchFlowModel/Compat.toml
+++ b/B/BranchFlowModel/Compat.toml
@@ -1,7 +1,6 @@
 [0]
 Graphs = "1.8.0-1"
 JSON = "0.21"
-MetaGraphs = "0.7"
 julia = "1.7.0-1"
 
 ["0-0.1"]
@@ -10,6 +9,9 @@ PowerModelsDistribution = "0.14"
 ["0-0.3.0"]
 JuMP = "1.9.0-1"
 
+["0-0.4.3"]
+MetaGraphs = "0.7"
+
 ["0.2"]
 CommonOPF = "0.2"
 
@@ -34,5 +36,9 @@ CommonOPF = "0.3.6-0.3"
 ["0.4.2"]
 CommonOPF = "0.3.7-0.3"
 
-["0.4.3-0"]
+["0.4.3"]
 CommonOPF = "0.3.8-0.3"
+
+["0.4.4-0"]
+CommonOPF = "0.4.1-0.4"
+MetaGraphsNext = "0.7"
diff --git a/B/BranchFlowModel/Deps.toml b/B/BranchFlowModel/Deps.toml
index 1f9b5c5f27a6cb7..f6530a146962ef4 100644
--- a/B/BranchFlowModel/Deps.toml
+++ b/B/BranchFlowModel/Deps.toml
@@ -3,12 +3,17 @@ Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-MetaGraphs = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 ["0-0.1"]
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 PowerModelsDistribution = "d7431456-977f-11e9-2de3-97ff7677985e"
 
+["0-0.4.3"]
+MetaGraphs = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
+
 ["0.2-0"]
 CommonOPF = "dad7ea18-2b21-482e-81c1-e84414cc4b03"
+
+["0.4.4-0"]
+MetaGraphsNext = "fa8bd995-216d-47f1-8a91-f3b68fbeb377"
diff --git a/B/BranchFlowModel/Versions.toml b/B/BranchFlowModel/Versions.toml
index 1576a73299ce28a..c45eb6e1323e22e 100644
--- a/B/BranchFlowModel/Versions.toml
+++ b/B/BranchFlowModel/Versions.toml
@@ -30,3 +30,6 @@ git-tree-sha1 = "3e7768f196d271e472862d3b54d43de077c7bb05"
 
 ["0.4.3"]
 git-tree-sha1 = "2270672b937d0233d3053d1d40cacc1eea4d10b1"
+
+["0.4.4"]
+git-tree-sha1 = "82ee66f12ccc587964ea3e3215be0a6ca0105647"