diff --git a/lib/graph.ex b/lib/graph.ex
index 78d1859..fae2255 100644
--- a/lib/graph.ex
+++ b/lib/graph.ex
@@ -1534,7 +1534,8 @@ defmodule Graph do
       [:d, :c, :b, :a]
   """
   @spec reachable(t, [vertex]) :: [[vertex]]
-  defdelegate reachable(g, vs), to: Graph.Directed
+  def reachable(%Graph{type: :undirected} = g, vs), do: Graph.Undirected.reachable(g, vs)
+  def reachable(%Graph{} = g, vs), do: Graph.Directed.reachable(g, vs)
 
   @doc """
   Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it `v`),
@@ -1550,7 +1551,10 @@ defmodule Graph do
       [:d, :c, :b]
   """
   @spec reachable_neighbors(t, [vertex]) :: [[vertex]]
-  defdelegate reachable_neighbors(g, vs), to: Graph.Directed
+  def reachable_neighbors(%Graph{type: :undirected} = g, vs),
+    do: Graph.Undirected.reachable_neighbors(g, vs)
+
+  def reachable_neighbors(%Graph{} = g, vs), do: Graph.Directed.reachable_neighbors(g, vs)
 
   @doc """
   Returns an unsorted list of vertices from the graph, such that for each vertex in the list (call it `v`),
diff --git a/lib/graph/undirected.ex b/lib/graph/undirected.ex
new file mode 100644
index 0000000..8da54e2
--- /dev/null
+++ b/lib/graph/undirected.ex
@@ -0,0 +1,91 @@
+defmodule Graph.Undirected do
+  @moduledoc false
+  @compile {:inline, [neighbors: 2, neighbors: 3]}
+
+  def reachable(%Graph{vertices: vertices, vertex_identifier: vertex_identifier} = g, vs)
+      when is_list(vs) do
+    vs = Enum.map(vs, vertex_identifier)
+    for id <- :lists.append(forest(g, &neighbors/3, vs, :first)), do: Map.get(vertices, id)
+  end
+
+  def reachable_neighbors(
+        %Graph{vertices: vertices, vertex_identifier: vertex_identifier} = g,
+        vs
+      )
+      when is_list(vs) do
+    vs = Enum.map(vs, vertex_identifier)
+
+    for id <- :lists.append(forest(g, &neighbors/3, vs, :not_first)),
+        do: Map.get(vertices, id)
+  end
+
+  def neighbors(%Graph{} = g, v, []) do
+    neighbors(g, v)
+  end
+
+  def neighbors(%Graph{out_edges: oe, in_edges: ie}, v, vs) do
+    case {Map.get(ie, v), Map.get(oe, v)} do
+      {nil, nil} ->
+        vs
+
+      {v_in, nil} ->
+        MapSet.to_list(v_in) ++ vs
+
+      {nil, v_out} ->
+        MapSet.to_list(v_out) ++ vs
+
+      {v_in, v_out} ->
+        s = MapSet.union(v_in, v_out)
+        MapSet.to_list(s) ++ vs
+    end
+  end
+
+  def neighbors(%Graph{out_edges: oe, in_edges: ie}, v) do
+    v_in = Map.get(ie, v, MapSet.new())
+    v_out = Map.get(oe, v, MapSet.new())
+
+    MapSet.union(v_in, v_out)
+    |> MapSet.to_list()
+  end
+
+  defp forest(%Graph{vertices: vs} = g, fun) do
+    forest(g, fun, Map.keys(vs))
+  end
+
+  defp forest(g, fun, vs) do
+    forest(g, fun, vs, :first)
+  end
+
+  defp forest(g, fun, vs, handle_first) do
+    {_, acc} =
+      List.foldl(vs, {MapSet.new(), []}, fn v, {visited, acc} ->
+        pretraverse(handle_first, v, fun, g, visited, acc)
+      end)
+
+    acc
+  end
+
+  defp pretraverse(:first, v, fun, g, visited, acc) do
+    ptraverse([v], fun, g, visited, [], acc)
+  end
+
+  defp pretraverse(:not_first, v, fun, g, visited, acc) do
+    if MapSet.member?(visited, v) do
+      {visited, acc}
+    else
+      ptraverse(fun.(g, v, []), fun, g, visited, [], acc)
+    end
+  end
+
+  defp ptraverse([v | vs], fun, g, visited, results, acc) do
+    if MapSet.member?(visited, v) do
+      ptraverse(vs, fun, g, visited, results, acc)
+    else
+      visited = MapSet.put(visited, v)
+      ptraverse(fun.(g, v, vs), fun, g, visited, [v | results], acc)
+    end
+  end
+
+  defp ptraverse([], _fun, _g, visited, [], acc), do: {visited, acc}
+  defp ptraverse([], _fun, _g, visited, results, acc), do: {visited, [results | acc]}
+end
diff --git a/test/undirected_graph_test.exs b/test/undirected_graph_test.exs
new file mode 100644
index 0000000..1a786e5
--- /dev/null
+++ b/test/undirected_graph_test.exs
@@ -0,0 +1,73 @@
+defmodule Graph.UndirectedTest do
+  use ExUnit.Case, async: true
+
+  describe "Graph.reachable/2" do
+    test "reachable" do
+      g =
+        Graph.new(type: :undirected)
+        |> Graph.add_edges([{:a, :b}, {:b, :c}])
+
+      assert [:a, :b, :c] = Graph.reachable(g, [:c])
+      assert [:c, :b, :a] = Graph.reachable(g, [:a])
+    end
+
+    test "parts reachable" do
+      g =
+        Graph.new(type: :undirected)
+        |> Graph.add_edges([{:a, :b}, {:b, :c}, {:d, :e}])
+
+      assert [:d, :e] = Graph.reachable(g, [:e])
+      assert [:c, :a, :b] = Graph.reachable(g, [:b])
+    end
+
+    test "nothing reachable" do
+      g =
+        Graph.new(type: :undirected)
+        |> Graph.add_edges([{:a, :b}, {:b, :d}])
+        |> Graph.add_vertex(:c)
+
+      assert [:c] = Graph.reachable(g, [:c])
+    end
+
+    test "unknown vertex" do
+      g = Graph.new(type: :undirected)
+
+      assert [nil] = Graph.reachable(g, [:a])
+    end
+  end
+
+  describe "Graph.reachable_neighbours/2" do
+    test "reachable" do
+      g =
+        Graph.new(type: :undirected)
+        |> Graph.add_edges([{:a, :b}, {:b, :c}])
+
+      assert [:a, :b] = Graph.reachable_neighbors(g, [:c])
+    end
+
+    @tag :only
+    test "parts reachable" do
+      g =
+        Graph.new(type: :undirected)
+        |> Graph.add_edges([{:a, :b}, {:b, :c}, {:d, :e}, {:e, :f}])
+
+      assert [:d, :e] = Graph.reachable_neighbors(g, [:f])
+      assert [] = Graph.reachable_neighbors(g, [:b])
+    end
+
+    test "nothing reachable" do
+      g =
+        Graph.new(type: :undirected)
+        |> Graph.add_edges([{:a, :b}, {:b, :d}])
+        |> Graph.add_vertex(:c)
+
+      assert [] = Graph.reachable_neighbors(g, [:c])
+    end
+
+    test "unknown vertex" do
+      g = Graph.new(type: :undirected)
+
+      assert [] = Graph.reachable_neighbors(g, [:a])
+    end
+  end
+end