diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 65a7604..cb50d10 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -55,7 +55,6 @@ jobs:
           flag-name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }}
           parallel: true
           path-to-lcov: lcov.info
-
   finish:
       name: Coveralls Finished
       needs: test
diff --git a/README.md b/README.md
index 91fe574..4bfc883 100644
--- a/README.md
+++ b/README.md
@@ -37,60 +37,72 @@ pkg> add UnitDiskMapping#master
 ```julia
 julia> using Graphs, UnitDiskMapping
 
-julia> g = smallgraph(:bull)
-{5, 5} undirected simple Int64 graph
+julia> g = smallgraph(:petersen)
+{10, 15} undirected simple Int64 graph
 
-julia> eg = embed_graph(g, 3)
-● ○ ● ○ ● ○ ◆ ○ ● ○ ● ○ ◆ ○ ● ○ ● ○ ◉ ○ ● ○ ● ○ ◉ 
-            ○           ○           ○           ○ 
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-            ● ○ ● ○ ● ○ ◆ ○ ● ○ ● ○ ◆ ○ ● ○ ● ○ ◉ 
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-                        ● ○ ● ○ ● ○ ◉ ○ ● ○ ● ○ ◆ 
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-                                                ○ 
-                                                ● 
-                                                ○ 
-                                                ● 
-                                                ○ 
-                                                ● 
+julia> res = map_graph(g, vertex_order=Branching());
 
-julia> apply_gadgets!(copy(eg))
-● ○ ● ○ ● ○   ○ ● ○ ● ○   ○ ● ○ ● ○ ○ ○ ● ○ ●     
-            ○           ○                         
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-              ○     ○ ○ ○       ○ ○ ○           ○ 
-                ● ○   ○   ○ ● ○   ○   ○ ● ○ ●   ○ 
-                      ○           ○             ○ 
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-                            ● ○ ● ○ ○ ○ ● ○ ● ○   
-                                  ○ ○ ○         ○ 
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-```
\ No newline at end of file
+julia> res.grid_graph
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ● ● ● ● ● ● ● ● ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ⋅ ● ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ● ● ● ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ● ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+
+julia> w_res = map_graph(Weighted(), g, vertex_order=Branching());
+
+julia> w_res.grid_graph
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ◯ ● ● ⋅ ● ● ● ● ● ● ● ● ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ⋅ ● ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ● ● ● ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ● ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ◯ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ● ● ● ● ● ⋅ ● ● ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ● ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 
+⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
+```
diff --git a/src/mapping.jl b/src/mapping.jl
index 5fdfaf8..2497db4 100644
--- a/src/mapping.jl
+++ b/src/mapping.jl
@@ -356,24 +356,31 @@ struct MappingResult{CT,WT}
 end
 
 """
-    map_graph([mode,] g::SimpleGraph; ruleset=[...])
+    map_graph([mode=Weighted(),] g::SimpleGraph; vertex_order=Greedy(), ruleset=[...])
 
-Map a graph to a unit disk grid graph that being "equivalent" to the original graph,
-where the optional argument `mode` can be `Weighted()` or `UnWeighted`.
+Map a graph to a unit disk grid graph that being "equivalent" to the original graph.
 Here "equivalent" means a maximum independent set in the grid graph can be mapped back to
 a maximum independent set of the original graph in polynomial time.
 
+
+* `mode` is optional, it can be `Weighted()` (default) or `UnWeighted`.
+* `vertex_order` specifies the order finding algorithm for vertices.
+Different vertex orders have different path width, i.e. different depth of mapped grid graph.
+It can be a vector or one of the following inputs
+    * `Greedy()` fast but not optimal.
+    * `Branching()` slow but optimal.
+* `ruleset` specifies and extra set of optimization patterns (not the crossing patterns).
+
 Returns a `MappingResult` instance.
 """
-map_graph(g::SimpleGraph; ruleset=[RotatedGadget(DanglingLeg(), n) for n=0:3]) = map_graph(UnWeighted(), g; ruleset=ruleset)
-function map_graph(mode, g::SimpleGraph; ruleset=[RotatedGadget(DanglingLeg(), n) for n=0:3])
-    ug = embed_graph(mode, g)
+map_graph(g::SimpleGraph; vertex_order=Greedy(), ruleset=[RotatedGadget(DanglingLeg(), n) for n=0:3]) = map_graph(UnWeighted(), g; ruleset=ruleset, vertex_order=vertex_order)
+function map_graph(mode, g::SimpleGraph; vertex_order=Greedy(), ruleset=[RotatedGadget(DanglingLeg(), n) for n=0:3])
+    ug = embed_graph(mode, g; vertex_order=vertex_order)
     mis_overhead0 = mis_overhead_copylines(ug)
     ug, tape = apply_crossing_gadgets!(mode, ug)
     ug, tape2 = apply_simplifier_gadgets!(ug; ruleset=ruleset)
     mis_overhead1 = isempty(tape) ? 0 : sum(x->mis_overhead(x[1]), tape)
     mis_overhead2 = isempty(tape2) ? 0 : sum(x->mis_overhead(x[1]), tape2)
-    @show mis_overhead0 , mis_overhead1 , mis_overhead2
     return MappingResult(ug, vcat(tape, tape2) , mis_overhead0 + mis_overhead1 + mis_overhead2)
 end
 
diff --git a/test/weighted.jl b/test/weighted.jl
index 1ba0c2e..fa5b6ed 100644
--- a/test/weighted.jl
+++ b/test/weighted.jl
@@ -14,12 +14,21 @@ using Random
         @assert length(locs1) == nv(g1)
         gp1 = Independence(g1, openvertices=pins1)
         gp2 = Independence(g2, openvertices=pins2)
-        m1 = mis_compactify!(missize(gp1, getfield.(locs1, :weight)))
-        m2 = mis_compactify!(missize(gp2, getfield.(locs2, :weight)))
+        w1 = getfield.(locs1, :weight)
+        w2 = getfield.(locs2, :weight)
+        w1[pins1] .-= 1
+        w2[pins2] .-= 1
+        m1 = missize(gp1, w1)
+        m2 = missize(gp2, w2)
+        mm1 = maximum(m1)
+        mm2 = maximum(m2)
         @test nv(g1) == length(locs1) && nv(g2) == length(locs2)
-        sig, diff = UnitDiskMapping.is_diff_by_const(content.(m1), content.(m2))
-        @test sig
-        @test diff == -mis_overhead(s)
+        if !(all((mm1 .== m1) .== (mm2 .== m2)))
+            @show m1
+            @show m2
+        end
+        @test all((mm1 .== m1) .== (mm2 .== m2))
+        @test content(mm1 / mm2) == -mis_overhead(s)
     end
 end