diff --git a/modules/core/src/main/scala/gs/graph/v0/directed/Dag.scala b/modules/core/src/main/scala/gs/graph/v0/directed/Dag.scala
index 3a25bf0..355d8e5 100644
--- a/modules/core/src/main/scala/gs/graph/v0/directed/Dag.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/directed/Dag.scala
@@ -18,6 +18,10 @@ class Dag protected (
 
 object Dag:
 
+  given CanEqual[Dag, Dag]     = CanEqual.derived
+  given CanEqual[Dag, Digraph] = CanEqual.derived
+  given CanEqual[Digraph, Dag] = CanEqual.derived
+
   /** Validate that the input [[Digraph]] is a DAG.
     *
     * @param digraph
@@ -26,7 +30,7 @@ object Dag:
     *   The DAG instance, or an error if the input contained a cycle.
     */
   def validate(digraph: Digraph): Either[GraphError, Dag] =
-    if Digraph.hasCycle(digraph) then
+    if !Digraph.hasCycle(digraph) then
       Right(
         new Dag(digraph.numberOfVertices, digraph.adjacency, digraph.roots)
       )
diff --git a/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala b/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala
index 318e94d..9ef9cd2 100644
--- a/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala
@@ -21,10 +21,26 @@ class Digraph(
   val adjacency: Adjacency,
   val roots: Vector[Vertex]
 ) extends Graph:
+  /** @inheritDocs
+    */
   override val disposition: GraphDisposition = GraphDisposition.Directed
 
+  override def equals(that: Any): Boolean =
+    that match
+      case other: Digraph =>
+        numberOfVertices == other.numberOfVertices
+        && adjacency == other.adjacency
+        && roots.sameElements(other.roots)
+      case _ => false
+
+end Digraph
+
 object Digraph:
 
+  given CanEqual[Digraph, Digraph] = CanEqual.derived
+
+  def empty(): Digraph = new Digraph(Size.Zero, Adjacency.Empty, Vector.empty)
+
   def fromEdges(
     numberOfVertices: Size,
     edges: Iterable[Edge]
@@ -85,8 +101,9 @@ object Digraph:
     */
   def hasCycle(digraph: Digraph): Boolean =
     digraph match
-      case _: Dag => false
-      case _      => new CycleDetector(digraph).hasCycle
+      case _ if digraph.isEmpty => false
+      case _: Dag               => false
+      case _                    => new CycleDetector(digraph).hasCycle
 
   // Internal class for finding cycles.
   // This implementation comes (roughly) from Algorithms (Fourth Edition) by
diff --git a/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala b/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala
new file mode 100644
index 0000000..115e998
--- /dev/null
+++ b/modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala
@@ -0,0 +1,11 @@
+package gs.graph.v0.directed
+
+import munit.*
+
+class DagTests extends FunSuite:
+
+  test("should validate an empty graph") {
+    Dag.validate(Digraph.empty()) match
+      case Right(dag) => assertEquals(dag, Digraph.empty())
+      case _ => fail("Expected the empty graph to be validated as a DAG.")
+  }