diff --git a/src/PeriodicGraphs.jl b/src/PeriodicGraphs.jl
index 2750204..b63e25e 100644
--- a/src/PeriodicGraphs.jl
+++ b/src/PeriodicGraphs.jl
@@ -984,5 +984,49 @@ function periodiccellgraph(g::PeriodicGraph)
     return ret
 end
 
+"""
+    dimensionality(g::PeriodicGraph)
+
+Determines the actual dimension of each connected component of `g`.
+Return a dictionary where each entry n => [l1, l2, ...] means that li is a
+list of vertices that form a connected component of dimension n.
+"""
+dimensionality(g::PeriodicGraph{0}) = Dict{Int,Vector{Vector{Int}}}(0 => [collect(vertices(g))])
+function dimensionality(g::PeriodicGraph{N}) where N
+    ret = Dict{Int,Vector{Vector{Int}}}()
+    n = nv(g)
+    visited = falses(n)
+    nullofs = zero(SVector{N,Int})
+    for i in vertices(g)
+        visited[i] && continue
+        recordedperiodicities = Set{SVector{N,Int}}()
+        component = Dict{Int,SVector{N,Int}}(i => nullofs)
+        seen = Set{PeriodicVertex{N}}([PeriodicVertex{N}(i)])
+        Q = PeriodicVertex[(PeriodicVertex{N}(i))]
+        for src in Q
+            @assert !visited[src.v]
+            for dst in outneighbors(g, src.v)
+                dst = PeriodicVertex{N}(dst.v, dst.ofs .+ src.ofs)
+                dst ∈ seen && continue
+                push!(seen, dst)
+                lastperiodicity = get!(component, dst.v, dst.ofs)
+                thisperiodicity = dst.ofs .- lastperiodicity
+                if iszero(thisperiodicity) # First time we encounter dst.v
+                    push!(Q, dst)
+                else
+                    push!(recordedperiodicities, thisperiodicity)
+                end
+            end
+        end
+        newcomponent = collect(keys(component))
+        visited[newcomponent] .= true
+        dim = rank(reduce(hcat, recordedperiodicities; init=reshape(nullofs, 3, 1)))
+        x = get!(ret, dim, [])
+        push!(x, newcomponent)
+    end
+    return ret
+end
+
+include("precompile.jl")
 
 end
diff --git a/src/precompile.jl b/src/precompile.jl
new file mode 100644
index 0000000..f462296
--- /dev/null
+++ b/src/precompile.jl
@@ -0,0 +1,43 @@
+function _precompile_()
+    ccall(:jl_generating_output, Cint, ()) == 1 || return nothing
+
+    Base.precompile(Tuple{Type{PeriodicGraph},String})
+
+    for i in 1:3
+        Base.precompile(Tuple{Type{PeriodicEdge{i}},Int,Int,NTuple{i, Int}})
+        Base.precompile(Tuple{Type{PeriodicVertex{i}},Int})
+        
+        Base.precompile(Tuple{Type{PeriodicEdge},Int,Int,NTuple{i, Int}})
+        Base.precompile(Tuple{Type{PeriodicEdge},Int,Int,SVector{i, Int}})
+        Base.precompile(Tuple{Type{PeriodicEdge},Int,PeriodicVertex{i}})
+
+        Base.precompile(Tuple{Type{PeriodicGraph{i}}})
+        Base.precompile(Tuple{Type{PeriodicGraph{i}},Vector{PeriodicEdge{i}}})
+        Base.precompile(Tuple{Type{PeriodicGraph{i}},String})
+
+        Base.precompile(Tuple{typeof(==),PeriodicVertex{i},PeriodicVertex{i}})
+        Base.precompile(Tuple{typeof(<),PeriodicVertex{i},PeriodicVertex{i}})
+        Base.precompile(Tuple{typeof(==),PeriodicEdge{i},PeriodicEdge{i}})
+        Base.precompile(Tuple{typeof(<),PeriodicEdge{i},PeriodicEdge{i}})
+
+        Base.precompile(Tuple{typeof(LightGraphs._neighborhood),PeriodicGraph{i},Int,Int,LightGraphs.DefaultDistance,Function})
+        Base.precompile(Tuple{typeof(add_edge!),PeriodicGraph{i},PeriodicEdge{i}})
+        Base.precompile(Tuple{typeof(add_vertices!),PeriodicGraph{i},Int})
+        Base.precompile(Tuple{typeof(rem_edge!),PeriodicGraph{i},PeriodicEdge{i}})
+        Base.precompile(Tuple{typeof(rem_vertex!),PeriodicGraph{i},Int})
+        Base.precompile(Tuple{typeof(connected_components),PeriodicGraph{i}})
+        Base.precompile(Tuple{typeof(coordination_sequence),PeriodicGraph{i},Int,Int})
+        Base.precompile(Tuple{typeof(dimensionality),PeriodicGraph{i}})
+        Base.precompile(Tuple{typeof(has_edge),PeriodicGraph{i},Int,Int})
+        Base.precompile(Tuple{typeof(induced_subgraph),PeriodicGraph{i},Vector{Int}})
+        Base.precompile(Tuple{typeof(isempty),PeriodicGraphs.PeriodicEdgeIter{i}})
+        Base.precompile(Tuple{typeof(neighborhood),PeriodicGraph{i},Int,Int})
+        Base.precompile(Tuple{typeof(offset_representatives!),PeriodicGraph{i},Vector{Int}})
+        Base.precompile(Tuple{typeof(reverse),PeriodicEdge{i}})
+        Base.precompile(Tuple{typeof(string),PeriodicEdge{i}})
+        Base.precompile(Tuple{typeof(string),PeriodicGraph{i}})
+        Base.precompile(Tuple{typeof(string),PeriodicVertex{i}})
+        Base.precompile(Tuple{typeof(swap_axes!),PeriodicGraph{i},Vector{Int}})
+        Base.precompile(Tuple{typeof(vertex_permutation),PeriodicGraph{i},Vector{Any}})
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 855f0e9..3900515 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,7 +1,7 @@
 using Test
 using LightGraphs
 using PeriodicGraphs
-import PeriodicGraphs: ofs, vertex_permutation, LoopException
+import PeriodicGraphs: ofs, vertex_permutation, dimensionality, LoopException
 import StaticArrays: SVector
 
 # using Aqua
@@ -355,3 +355,35 @@ end
     @test rem_vertex!(gg, 2)
     @test g == gg
 end
+
+@testset "Dimensionality" begin
+    @test dimensionality(PeriodicGraph{0}(5)) == Dict(0 => [collect(1:5)])
+    g::PeriodicGraph3D = PeriodicGraph3D([PeriodicEdge3D(1, 3, (0, 0, 1)),
+                                          PeriodicEdge3D(2, 3, (0, 1, 0)),
+                                          PeriodicEdge3D(2, 3, (0, -1, 0)),
+                                          PeriodicEdge3D(4, 4, (1, 1, 0))])
+    function equivalent_dict(d1, d2)
+        keys(d1) == keys(d2) || return false
+        for k in keys(d1)
+            s1 = Set(Set(x) for x in d1[k])
+            s2 = Set(Set(x) for x in d2[k])
+            s1 == s2 || return false
+        end
+        return true
+    end
+    @test equivalent_dict(dimensionality(g), Dict(1 => connected_components(g)))
+    @test add_edge!(g, PeriodicEdge(3, 2, (0,0,0)))
+    @test equivalent_dict(dimensionality(g), Dict(1 => connected_components(g)))
+    @test add_edge!(g, PeriodicEdge(2, 2, (0,0,1)))
+    @test equivalent_dict(dimensionality(g), Dict(1 => [[4]], 2 => [[1,2,3]]))
+    @test rem_edge!(g, PeriodicEdge(1, 3, (0,0,1)))
+    @test equivalent_dict(dimensionality(g), Dict(0 => [[1]], 1 => [[4]], 2 => [[2,3]]))
+    @test rem_edge!(g, PeriodicEdge(3, 2, (0,0,0)))
+    @test equivalent_dict(dimensionality(g), Dict(0 => [[1]], 1 => [[4]], 2 => [[2,3]]))
+    @test rem_edge!(g, PeriodicEdge(2, 3, (0,1,0)))
+    @test equivalent_dict(dimensionality(g), Dict(0 => [[1]], 1 => [[2,3],[4]]))
+    @test add_edge!(g, PeriodicEdge(2, 3, (1,0,-1)))
+    @test equivalent_dict(dimensionality(g), Dict(0 => [[1]], 1 => [[4]], 2 => [[2,3]]))
+    @test add_edge!(g, PeriodicEdge(2, 3, (2,0,-1)))
+    @test equivalent_dict(dimensionality(g), Dict(0 => [[1]], 1 => [[4]], 3 => [[2,3]]))
+end