diff --git a/src/categorical_algebra/FinCats.jl b/src/categorical_algebra/FinCats.jl
index 30c3254d2..e05054548 100644
--- a/src/categorical_algebra/FinCats.jl
+++ b/src/categorical_algebra/FinCats.jl
@@ -25,13 +25,14 @@ using DataStructures: IntDisjointSets, in_same_set, num_groups
 using ACSets
 using ...GATs
 import ...GATs: equations
-using ...Theories: ThCategory, ThSchema, ThPointedSetCategory, ThPointedSetSchema, ObExpr, HomExpr, AttrExpr, AttrTypeExpr, FreeSchema, FreePointedSetCategory, zeromap
+using ...Theories: ThCategory, ThSchema, ThPointedSetCategory, ThPointedSetSchema,
+  ObExpr, HomExpr, AttrExpr, AttrTypeExpr, FreeSchema, FreePointedSetCategory, zeromap
 import ...Theories: dom, codom, id, compose, ⋅, ∘
 using ...Graphs
 import ...Graphs: edges, src, tgt, enumerate_paths
-import ...Graphs.BasicGraphs: vertex_named, vertex_name, DiagramGraph, edge_named, edge_name
 @reexport using ..Categories
 import ..Categories: CatSize, ob, hom, ob_map, hom_map, component, op
+
 # Categories
 ############
 
@@ -110,7 +111,7 @@ hom generators are indexable, other
 than one explicitly generated by a graph.
 """
 function graph(C::FinCat) 
-  g =  DiagramGraph() 
+  g = NamedGraph{Symbol,Symbol}()
   obgens = ob_generators(C)
   homgens = hom_generators(C)
   add_vertices!(g,length(obgens);vname=nameof.(obgens))
diff --git a/src/categorical_algebra/FunctorialDataMigrations.jl b/src/categorical_algebra/FunctorialDataMigrations.jl
index dcfd4d2c0..b69b0a053 100644
--- a/src/categorical_algebra/FunctorialDataMigrations.jl
+++ b/src/categorical_algebra/FunctorialDataMigrations.jl
@@ -6,22 +6,19 @@ export SigmaMigration, DeltaMigration, migrate, migrate!,
   internal_hom, SigmaMigrationFunctor, DeltaMigrationFunctor, 
   DataMigrationFunctor, functor
 
-#maybe should only define DeltaMigrationFunctor at this point
+using MLStyle: @match
+
 using ACSets
 using ACSets.DenseACSets: constructor, datatypes
 using ...GATs
 using ...Theories: ob, hom, dom, codom, attr, AttrTypeExpr, ⋅
 using ..Categories, ..FinCats, ..Limits, ..Diagrams, ..FinSets, ..CSets, ..HomSearch
 using ...Graphs, ..FreeDiagrams
-using ...Graphs.BasicGraphs: NamedGraph, vertex_named
 import ..Categories: ob_map, hom_map
 import ...GATs: functor
 using ..FinCats: make_map, mapvals, presentation_key
-using ..Diagrams
-import ..FinCats: FinCatPresentation
 using ..Chase: collage, crel_type, pres_to_eds, add_srctgt, chase
 using ..FinSets: VarSet
-using MLStyle: @match
 
 # Data types
 ############
diff --git a/src/graphs/BasicGraphs.jl b/src/graphs/BasicGraphs.jl
index 1e67bb462..092a87f51 100644
--- a/src/graphs/BasicGraphs.jl
+++ b/src/graphs/BasicGraphs.jl
@@ -1,10 +1,14 @@
 """ Data structures for graphs, based on C-sets.
 
-Provides the category theorist's four basic kinds of graphs: graphs (aka
-directed multigraphs), symmetric graphs, reflexive graphs, and symmetric
-reflexive graphs. Also defines half-edge graphs. The API generally follows that
-of [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl), with some departures
-due to differences between the data structures.
+This module provides the category theorist's four basic kinds of graphs: graphs
+(aka directed multigraphs), symmetric graphs, reflexive graphs, and symmetric
+reflexive graphs. It also defines half-edge graphs, which are isomorphic to
+symmetric graphs, and a few standard kinds of attributed graphs, such as
+weighted graphs.
+
+The graphs API generally follows that of
+[Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl), with some departures due
+to differences between the data structures.
 """
 module BasicGraphs
 export HasVertices, HasGraph, AbstractGraph, Graph, SchGraph,
@@ -117,6 +121,7 @@ has_vertex(g::HasVertices, v) = has_part(g, :V, v)
 """ Whether the graph has the given edge, or an edge between two vertices.
 """
 has_edge(g::HasGraph, e) = has_part(g, :E, e)
+
 function has_edge(g::HasGraph, s::Int, t::Int)
   (1 <= s <= nv(g)) || return false
   for e in outedges(g,s)
@@ -572,32 +577,4 @@ function Base.reverse!(g::G) where G<:HasGraph
 end
 Base.reverse(g::G) where G<:HasGraph = g |> deepcopy |> reverse!
 
-vertex_name(G::HasGraph, v) = v
-edge_name(G::HasGraph, e) = e
-
-@present SchNamedGraph <: SchGraph begin
-  VName::AttrType
-  EName::AttrType
-  vname::Attr(V, VName)
-  ename::Attr(E, EName)
-end
-
-""" Abstract type for graph with named vertices and edges.
-"""
-@abstract_acset_type AbstractNamedGraph <: AbstractGraph
-
-""" Graph with named vertices and edges.
-The default graph type used to construct the graph underlying
-a finite category given by a presentation.
-"""
-@acset_type NamedGraph(SchNamedGraph, index=[:src,:tgt,:ename],
-                       unique_index=[:vname]) <: AbstractNamedGraph
-vertex_name(g::AbstractNamedGraph, args...) = subpart(g, args..., :vname)
-edge_name(g::AbstractNamedGraph, args...) = subpart(g, args..., :ename)
-
-vertex_named(g::AbstractNamedGraph, name) = only(incident(g, name, :vname))
-edge_named(g::AbstractNamedGraph, name)= only(incident(g, name, :ename))
-const DiagramGraph = NamedGraph{Symbol,Symbol}
-
-
 end # module
diff --git a/src/graphs/Searching.jl b/src/graphs/GraphSearching.jl
similarity index 99%
rename from src/graphs/Searching.jl
rename to src/graphs/GraphSearching.jl
index 3b675cf3a..d35e47bc8 100644
--- a/src/graphs/Searching.jl
+++ b/src/graphs/GraphSearching.jl
@@ -1,4 +1,4 @@
-module Searching
+module GraphSearching
 export bfs_parents, bfs_tree, dfs_parents, dfs_tree
 
 using ACSets
diff --git a/src/graphs/Graphs.jl b/src/graphs/Graphs.jl
index 300056816..520538b41 100644
--- a/src/graphs/Graphs.jl
+++ b/src/graphs/Graphs.jl
@@ -4,16 +4,18 @@ using Reexport
 
 include("BasicGraphs.jl")
 include("BipartiteGraphs.jl")
+include("NamedGraphs.jl")
 include("PropertyGraphs.jl")
 include("GraphAlgorithms.jl")
 include("GraphGenerators.jl")
-include("Searching.jl")
+include("GraphSearching.jl")
 
 @reexport using .BasicGraphs
 @reexport using .BipartiteGraphs
+@reexport using .NamedGraphs
 @reexport using .PropertyGraphs
 @reexport using .GraphAlgorithms
 @reexport using .GraphGenerators
-@reexport using .Searching
+@reexport using .GraphSearching
 
 end
diff --git a/src/graphs/NamedGraphs.jl b/src/graphs/NamedGraphs.jl
new file mode 100644
index 000000000..bfedb75d6
--- /dev/null
+++ b/src/graphs/NamedGraphs.jl
@@ -0,0 +1,69 @@
+""" Extends the basic graph types with vertex and/or edge names.
+
+Naming vertices and edges and looking them up by name is a common requirement.
+This module provides a simple interface and default graph types for named
+graphs. Names are understood to be unique within the graph but are *not* assumed
+to be strings or symbols.
+"""
+module NamedGraphs
+export vertex_name, edge_name, vertex_named, edge_named,
+  AbstractNamedGraph, NamedGraph
+
+using ACSets
+using ...GATs, ..BasicGraphs
+
+# Names interface
+#################
+
+""" Name of a vertex in a graph.
+
+By default, the name of a vertex is its ID.
+"""
+vertex_name(g::HasVertices, v) = v
+
+""" Name of an edge in a graph.
+
+By default, the name of an edge is its ID.
+"""
+edge_name(g::HasGraph, e) = e
+
+""" Get vertex in graph with given name.
+"""
+function vertex_named(g::HasVertices, name)
+  @assert has_vertex(g, name)
+  name
+end
+
+""" Get edge in graph with given name.
+"""
+function edge_named(g::HasGraph, name)
+  @assert has_edge(g, name)
+  name
+end
+
+# Named graphs
+##############
+
+@present SchNamedGraph <: SchGraph begin
+  VName::AttrType
+  EName::AttrType
+  vname::Attr(V, VName)
+  ename::Attr(E, EName)
+end
+
+""" Abstract type for graph with named vertices and edges.
+"""
+@abstract_acset_type AbstractNamedGraph <: AbstractGraph
+
+""" Graph with named vertices and edges.
+"""
+@acset_type NamedGraph(SchNamedGraph, index=[:src,:tgt,:ename],
+                       unique_index=[:vname]) <: AbstractNamedGraph
+
+vertex_name(g::AbstractNamedGraph, args...) = subpart(g, args..., :vname)
+edge_name(g::AbstractNamedGraph, args...) = subpart(g, args..., :ename)
+
+vertex_named(g::AbstractNamedGraph, name) = only(incident(g, name, :vname))
+edge_named(g::AbstractNamedGraph, name)= only(incident(g, name, :ename))
+
+end
diff --git a/test/graphs/GraphAlgorithms.jl b/test/graphs/GraphAlgorithms.jl
index d7941b20d..dd042f24f 100644
--- a/test/graphs/GraphAlgorithms.jl
+++ b/test/graphs/GraphAlgorithms.jl
@@ -72,17 +72,4 @@ ep = enumerate_paths(g)
     (2, 3, [3])
     (3, 3, [])]
 
-# Trees
-#######
-
-g = Searching.tree([1, 1, 1, 2, 2])
-g′ = @acset Graph begin
-  V = 5
-  E = 4
-  src = [1, 1, 2, 2]
-  tgt = [2, 3, 4, 5]
-end
-
-@test is_isomorphic(g,g′)
-
 end
diff --git a/test/graphs/Searching.jl b/test/graphs/GraphSearching.jl
similarity index 60%
rename from test/graphs/Searching.jl
rename to test/graphs/GraphSearching.jl
index 7a4482add..529091e20 100644
--- a/test/graphs/Searching.jl
+++ b/test/graphs/GraphSearching.jl
@@ -1,10 +1,9 @@
-module TestSearching
+module TestGraphSearching
 using Test
 
-using Catlab.Graphs.BasicGraphs, Catlab.Graphs.Searching
-import Catlab.Graphs.Searching: tree
-
-# Tests stolen from Graphs.jl
+using Catlab.Graphs.BasicGraphs, Catlab.Graphs.GraphSearching
+using Catlab.Graphs.GraphSearching: tree
+using Catlab.CategoricalAlgebra: @acset, is_isomorphic
 
 # BFS
 #----
@@ -24,8 +23,7 @@ parents = bfs_parents(g, 1)
 t1 = @inferred(bfs_tree(g, 1))
 t2 = tree(parents)
 @test t1 == t2
-@test is_directed(t2)
-@test typeof(t2) <: AbstractGraph
+@test t2 isa AbstractGraph
 @test ne(t2) < nv(t2)
 
 # DFS
@@ -36,6 +34,17 @@ add_edges!(g, [1,2,1,3], [2,3,3,4])
 z = @inferred(dfs_tree(g, 1))
 @test ne(z) == 3 && nv(z) == 4
 @test !has_edge(z, 1, 3)
-@test !is_cyclic(g)
+
+# Trees
+#------
+
+g = tree([1, 1, 1, 2, 2])
+g′ = @acset Graph begin
+  V = 5
+  E = 4
+  src = [1, 1, 2, 2]
+  tgt = [2, 3, 4, 5]
+end
+@test is_isomorphic(g, g′)
 
 end
diff --git a/test/graphs/Graphs.jl b/test/graphs/Graphs.jl
index 7285f148d..512113209 100644
--- a/test/graphs/Graphs.jl
+++ b/test/graphs/Graphs.jl
@@ -10,6 +10,10 @@ end
   include("BipartiteGraphs.jl")
 end
 
+@testset "NamedGraphs" begin
+  include("NamedGraphs.jl")
+end
+
 @testset "PropertyGraphs" begin
   include("PropertyGraphs.jl")
 end
@@ -22,4 +26,8 @@ end
   include("GraphGenerators.jl")
 end
 
+@testset "GraphSearching" begin
+  include("GraphSearching.jl")
+end
+
 end
diff --git a/test/graphs/NamedGraphs.jl b/test/graphs/NamedGraphs.jl
new file mode 100644
index 000000000..258d0e9cc
--- /dev/null
+++ b/test/graphs/NamedGraphs.jl
@@ -0,0 +1,25 @@
+module TestNamedGraphs
+using Test
+
+using Catlab.Graphs
+
+# Basic graphs
+##############
+
+g = path_graph(Graph, 3)
+@test vertex_name(g, 2) == 2
+@test vertex_named(g, 2) == 2
+@test edge_name(g, 1) == 1
+@test edge_named(g, 1) == 1
+
+# Named graphs
+##############
+
+g = path_graph(NamedGraph{Symbol,Symbol}, 3,
+               V=(vname=[:x,:y,:z],), E=(ename=[:f,:g],))
+@test vertex_name(g, 2) == :y
+@test vertex_named(g, :y) == 2
+@test edge_name(g, 1) == :f
+@test edge_named(g, :f) == 1
+
+end