diff --git a/Project.toml b/Project.toml
index 5aaa4d7..7dd2354 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,14 +1,16 @@
 name = "MetaGraphsNext"
 uuid = "fa8bd995-216d-47f1-8a91-f3b68fbeb377"
-version = "0.4.1"
+version = "0.5.0"
 
 [deps]
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
+SimpleTraits = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
 
 [compat]
 Graphs = "1.4.1"
 JLD2 = "0.1.11, 0.2, 0.3, 0.4"
+SimpleTraits = "0.9"
 julia = "1.6"
 
 [extras]
diff --git a/src/MetaGraphsNext.jl b/src/MetaGraphsNext.jl
index 219a393..4bba836 100644
--- a/src/MetaGraphsNext.jl
+++ b/src/MetaGraphsNext.jl
@@ -2,15 +2,15 @@ module MetaGraphsNext
 
 using JLD2
 using Graphs
+using SimpleTraits
 
-export MetaGraph, MetaDiGraph, MetaUndirectedGraph
+export MetaGraph
 export label_for, code_for, set_data!
 export weighttype, default_weight, get_weight_function
 export MGFormat, DOTFormat
 
 include("metagraph.jl")
-include("metaundigraph.jl")
-include("metadigraph.jl")
+include("directedness.jl")
 include("graphs.jl")
 include("dict_utils.jl")
 include("weights.jl")
diff --git a/src/directedness.jl b/src/directedness.jl
new file mode 100644
index 0000000..d2af739
--- /dev/null
+++ b/src/directedness.jl
@@ -0,0 +1,34 @@
+"""
+    arrange(graph, label_1, label_2)
+
+Sort two vertex labels in a default order (useful to uniquely express undirected edges).
+"""
+function arrange end
+
+@traitfn function arrange(
+    ::AG::IsDirected, label_1, label_2, _drop...
+) where {T,AG<:AbstractGraph{T}}
+    return label_1, label_2
+end
+
+@traitfn function arrange(
+    ::AG::(!IsDirected), label_1, label_2, code_1, code_2
+) where {T,AG<:AbstractGraph{T}}
+    if code_1 < code_2
+        (label_1, label_2)
+    else
+        (label_2, label_1)
+    end
+end
+
+@traitfn function arrange(
+    meta_graph::AG::(!IsDirected), label_1, label_2
+) where {T,AG<:AbstractGraph{T}}
+    return arrange(
+        meta_graph,
+        label_1,
+        label_2,
+        code_for(meta_graph, label_1),
+        code_for(meta_graph, label_2),
+    )
+end
diff --git a/src/graphs.jl b/src/graphs.jl
index 0fd4e50..4eb85ba 100644
--- a/src/graphs.jl
+++ b/src/graphs.jl
@@ -41,6 +41,18 @@ function Base.issubset(meta_graph::MetaGraph, h::MetaGraph)
     return issubset(meta_graph.graph, h.graph)
 end
 
+function Graphs.is_directed(
+    ::MetaGraph{Code,Label,Graph}
+) where {Code,Label,Graph<:AbstractGraph}
+    return is_directed(Graph)
+end
+
+function Graphs.is_directed(
+    ::Type{<:MetaGraph{Code,Label,Graph}}
+) where {Code,Label,Graph<:AbstractGraph}
+    return is_directed(Graph)
+end
+
 ## Link between graph codes and metagraph labels
 
 """
@@ -210,7 +222,7 @@ function Graphs.induced_subgraph(
     return new_graph, code_map
 end
 
-function Graphs.reverse(meta_graph::MetaDiGraph)
+@traitfn function Graphs.reverse(meta_graph::MetaGraph::IsDirected)
     edge_data = meta_graph.edge_data
     reverse_edge_data = empty(edge_data)
     for (label_1, label_2) in keys(edge_data)
diff --git a/src/metadigraph.jl b/src/metadigraph.jl
deleted file mode 100644
index d790968..0000000
--- a/src/metadigraph.jl
+++ /dev/null
@@ -1,21 +0,0 @@
-"""
-    MetaDiGraph
-
-A `MetaGraph` whose underlying graph is of type `Graphs.SimpleDiGraph`.
-"""
-const MetaDiGraph = MetaGraph{<:Any,<:Any,<:SimpleDiGraph}
-
-function Graphs.SimpleDiGraph(meta_graph::MetaDiGraph)
-    return meta_graph.graph
-end
-
-function Graphs.is_directed(::Type{<:MetaDiGraph})
-    return true
-end
-function Graphs.is_directed(::MetaDiGraph)
-    return true
-end
-
-function arrange(::MetaDiGraph, label_1, label_2, _...)
-    return label_1, label_2
-end
diff --git a/src/metagraph.jl b/src/metagraph.jl
index c11c223..a7082fb 100644
--- a/src/metagraph.jl
+++ b/src/metagraph.jl
@@ -1,5 +1,14 @@
 """
-    MetaGraph{Code<:Integer,Label,Graph,VertexData,EdgeData,GraphData,WeightFunction,Weight<:Real} <: AbstractGraph{Code}
+    MetaGraph{
+        Code<:Integer,
+        Label,
+        Graph,
+        VertexData,
+        EdgeData,
+        GraphData,
+        WeightFunction,
+        Weight<:Real
+    } <: AbstractGraph{Code}
 
 A graph type with custom vertex labels containing vertex-, edge- and graph-level metadata.
 
@@ -65,13 +74,6 @@ function MetaGraph(
     )
 end
 
-"""
-    arrange(graph, label_1, label_2)
-
-Sort two vertex labels in a default order (useful to uniquely express undirected edges).
-"""
-function arrange end
-
 function Base.zero(
     meta_graph::MetaGraph{Code,Label,Graph,VertexData,EdgeData}
 ) where {Code,Label,Graph,VertexData,EdgeData}
diff --git a/src/metaundigraph.jl b/src/metaundigraph.jl
deleted file mode 100644
index 904dee4..0000000
--- a/src/metaundigraph.jl
+++ /dev/null
@@ -1,29 +0,0 @@
-"""
-    MetaUndirectedGraph
-
-A `MetaGraph` whose underlying graph is of type `Graphs.SimpleGraph`.
-"""
-const MetaUndirectedGraph = MetaGraph{<:Any,<:Any,<:SimpleGraph}
-
-Graphs.SimpleGraph(meta_graph::MetaUndirectedGraph) = meta_graph.graph
-
-Graphs.is_directed(::Type{<:MetaUndirectedGraph}) = false
-Graphs.is_directed(::MetaUndirectedGraph) = false
-
-function arrange(::MetaUndirectedGraph, label_1, label_2, code_1, code_2)
-    if code_1 < code_2
-        (label_1, label_2)
-    else
-        (label_2, label_1)
-    end
-end
-
-function arrange(meta_graph::MetaUndirectedGraph, label_1, label_2)
-    return arrange(
-        meta_graph,
-        label_1,
-        label_2,
-        code_for(meta_graph, label_1),
-        code_for(meta_graph, label_2),
-    )
-end
diff --git a/test/labels_codes.jl b/test/labels_codes.jl
deleted file mode 100644
index 1a5c31b..0000000
--- a/test/labels_codes.jl
+++ /dev/null
@@ -1,21 +0,0 @@
-using MetaGraphsNext
-
-colors = MetaGraph(
-    Graph(); VertexData=String, EdgeData=Symbol, graph_data="graph_of_colors"
-)
-
-labels = [:red, :yellow, :blue]
-values = ["warm", "warm", "cool"]
-for (label, value) in zip(labels, values)
-    colors[label] = value
-end
-for label in labels
-    @test label_for(colors, code_for(colors, label)) == label
-end
-#delete an entry and test again
-rem_vertex!(colors, 1)
-popfirst!(labels)
-popfirst!(values)
-for label in labels
-    @test label_for(colors, code_for(colors, label)) == label
-end
diff --git a/test/labels_codes_directedness.jl b/test/labels_codes_directedness.jl
new file mode 100644
index 0000000..f1c0f0a
--- /dev/null
+++ b/test/labels_codes_directedness.jl
@@ -0,0 +1,34 @@
+# undirected MetaGraph
+colors = MetaGraph(
+    Graph(); VertexData=String, EdgeData=Symbol, graph_data="graph_of_colors"
+)
+@test istrait(IsDirected{typeof(colors)}) == is_directed(colors) == false
+labels = [:red, :yellow, :blue]
+values = ["warm", "warm", "cool"]
+for (label, value) in zip(labels, values)
+    colors[label] = value
+end
+for label in labels
+    @test label_for(colors, code_for(colors, label)) == label
+end
+#delete an entry and test again
+rem_vertex!(colors, 1)
+popfirst!(labels)
+popfirst!(values)
+for label in labels
+    @test label_for(colors, code_for(colors, label)) == label
+end
+@test MetaGraphsNext.arrange(colors, :yellow, :blue) == (:blue, :yellow)
+
+# directed MetaGraph
+dcolors = MetaGraph(
+    SimpleDiGraph(); VertexData=String, EdgeData=Symbol, graph_data="graph_of_colors"
+)
+@test istrait(IsDirected{typeof(dcolors)}) == is_directed(dcolors) == true
+labels = [:red, :yellow, :blue]
+values = ["warm", "warm", "cool"]
+for (label, value) in zip(labels, values)
+    dcolors[label] = value
+end
+dcolors[:red, :yellow] = :redyellow
+@test MetaGraphsNext.arrange(dcolors, :yellow, :blue) == (:yellow, :blue)
diff --git a/test/runtests.jl b/test/runtests.jl
index 72012c2..a3649d1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,6 +3,7 @@ using Documenter
 using Graphs
 using JuliaFormatter
 using MetaGraphsNext
+using SimpleTraits
 using Test
 
 @testset verbose = true "MetaGraphsNext" begin
@@ -26,7 +27,7 @@ using Test
             include(joinpath("tutorial", "3_files.jl"))
         end
     end
-    @testset verbose = true "Labels and codes" begin
-        include("labels_codes.jl")
+    @testset verbose = true "Labels, codes, directedness" begin
+        include("labels_codes_directedness.jl")
     end
 end
diff --git a/test/tutorial/2_graphs.jl b/test/tutorial/2_graphs.jl
index 8324914..cb5651d 100644
--- a/test/tutorial/2_graphs.jl
+++ b/test/tutorial/2_graphs.jl
@@ -39,8 +39,6 @@ eltype(cities)
 #-
 edgetype(cities)
 @test edgetype(cities) == Graphs.SimpleEdge{Int}  #src
-#-
-SimpleGraph(cities)
 
 # We can check the set of vertices:
 
@@ -121,8 +119,6 @@ rock_paper_scissors[:paper, :rock] = "paper beats rock";
 
 is_directed(rock_paper_scissors)
 @test is_directed(rock_paper_scissors)  #src
-#-
-SimpleDiGraph(rock_paper_scissors)
 
 # Directed graphs can be reversed: