diff --git a/modules/core/src/main/scala/gs/graph/v0/Edge.scala b/modules/core/src/main/scala/gs/graph/v0/Edge.scala
index 71d2435..ef91269 100644
--- a/modules/core/src/main/scala/gs/graph/v0/Edge.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/Edge.scala
@@ -2,7 +2,7 @@ package gs.graph.v0
 
 import java.util.Objects
 
-/** Represents a relationship between two [[Vertex]].
+/** Represents a relationship between two distinct [[Vertex]].
   *
   * When used is a directed context, the edge goes _from_ `v1` _to_ `v2`.
   *
@@ -11,7 +11,7 @@ import java.util.Objects
   * @param v2
   *   The second [[Vertex]].
   */
-final class Edge(
+final class Edge private (
   val v1: Vertex,
   val v2: Vertex
 ):
@@ -54,11 +54,53 @@ object Edge:
 
   given CanEqual[Edge, Edge] = CanEqual.derived
 
+  /** Instantiate a new Edge.
+    *
+    * Throws an exception if the given vertices are the same.
+    *
+    * @param v1
+    *   The first [[Vertex]].
+    * @param v2
+    *   The second [[Vertex]].
+    * @return
+    *   The new edge.
+    */
   def apply(
     v1: Vertex,
     v2: Vertex
-  ): Edge = new Edge(v1, v2)
+  ): Edge =
+    if v1 != v2 then new Edge(v1, v2)
+    else
+      throw new IllegalArgumentException(
+        "Loop edges are not supported. Edges must refer to two distinct vertexes."
+      )
 
-  def apply(vs: (Vertex, Vertex)): Edge = new Edge(vs._1, vs._2)
+  /** Instantiate a new Edge.
+    *
+    * Throws an exception if the given vertices are the same.
+    *
+    * @param vs
+    *   The pair of [[Vertex]].
+    * @return
+    *   The new edge.
+    */
+  def apply(vs: (Vertex, Vertex)): Edge = Edge(vs._1, vs._2)
+
+  /** Instantiate a new Edge.
+    *
+    * Throws an exception if the given vertices are the same or are not valid
+    * [[Vertex]] values.
+    *
+    * @param v1
+    *   The first [[Vertex]].
+    * @param v2
+    *   The second [[Vertex]].
+    * @return
+    *   The new edge.
+    */
+  def apply(
+    v1: Int,
+    v2: Int
+  ): Edge = Edge(Vertex(v1), Vertex(v2))
 
 end Edge
diff --git a/modules/core/src/main/scala/gs/graph/v0/directed/SCC.scala b/modules/core/src/main/scala/gs/graph/v0/SCC.scala
similarity index 92%
rename from modules/core/src/main/scala/gs/graph/v0/directed/SCC.scala
rename to modules/core/src/main/scala/gs/graph/v0/SCC.scala
index ce46957..c0669f4 100644
--- a/modules/core/src/main/scala/gs/graph/v0/directed/SCC.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/SCC.scala
@@ -1,4 +1,4 @@
-package gs.graph.v0.directed
+package gs.graph.v0
 
 import gs.graph.v0.Graph
 import gs.graph.v0.Vertex
@@ -45,11 +45,20 @@ object SCC:
       */
     def isSingle: Boolean = scc.size == 1
 
-  /** Implementation of Tarjan's Algorithm for finding all strongly connected
-    * components for some directed graph.
+  /** Alias for `findAll`.
     *
     * @param g
-    *   The directed graph to analyze.
+    *   The graph to analyze.
+    * @return
+    *   The complete list of [[SCC]] for the input graph.
+    */
+  def tarjan(g: Graph): List[SCC] = findAll(g)
+
+  /** Implementation of Tarjan's Algorithm for finding all strongly connected
+    * components for some graph.
+    *
+    * @param g
+    *   The graph to analyze.
     * @return
     *   The complete list of [[SCC]] for the input graph.
     */
diff --git a/modules/core/src/main/scala/gs/graph/v0/Size.scala b/modules/core/src/main/scala/gs/graph/v0/Size.scala
index e98c192..6c47402 100644
--- a/modules/core/src/main/scala/gs/graph/v0/Size.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/Size.scala
@@ -83,17 +83,6 @@ object Size:
     if candidate >= 0 then new Size(candidate)
     else throw new IllegalArgumentException("Size values must be 0 or greater.")
 
-  given CanEqual[Size, Size] = CanEqual.derived
-
-  given Ordering[Size] with
-
-    /** @inheritDocs
-      */
-    def compare(
-      x: Size,
-      y: Size
-    ): Int = x.value - y.value
-
   /** Instantiate the size of some array.
     *
     * @param arr
@@ -112,4 +101,15 @@ object Size:
     */
   def fromVector(vec: Vector[?]): Size = new Size(vec.length)
 
+  given CanEqual[Size, Size] = CanEqual.derived
+
+  given Ordering[Size] with
+
+    /** @inheritDocs
+      */
+    def compare(
+      x: Size,
+      y: Size
+    ): Int = x.value - y.value
+
 end Size
diff --git a/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala b/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala
index 4795f5d..d7e9618 100644
--- a/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala
+++ b/modules/core/src/main/scala/gs/graph/v0/UndirectedGraph.scala
@@ -17,8 +17,24 @@ class UndirectedGraph(
 
   /** @inheritDocs
     */
-  override def selectRoots(): Vector[Vertex] =
-    if numberOfVertices == Size.Zero then Vector.empty else Vector(Vertex.Zero)
+  override def selectRoots(): Vector[Vertex] = roots
+
+  /** The roots of an undirected graph are identified by arbitrarily selecting
+    * the first listed vertex from each strongly connected component in the
+    * graph.
+    */
+  lazy val roots: Vector[Vertex] =
+    calculateRoots()
+
+  private def calculateRoots(): Vector[Vertex] =
+    if numberOfVertices == Size.Zero then Vector.empty
+    else oneRootFromEachSCC(calculateSCCs()).toVector
+
+  private def calculateSCCs(): List[SCC] =
+    SCC.findAll(this)
+
+  private def oneRootFromEachSCC(sccs: List[SCC]): List[Vertex] =
+    sccs.map(_.vertices.apply(0))
 
 end UndirectedGraph
 
diff --git a/modules/core/src/test/scala/gs/graph/v0/EdgeTests.scala b/modules/core/src/test/scala/gs/graph/v0/EdgeTests.scala
new file mode 100644
index 0000000..94b1e81
--- /dev/null
+++ b/modules/core/src/test/scala/gs/graph/v0/EdgeTests.scala
@@ -0,0 +1,24 @@
+package gs.graph.v0
+
+import munit.*
+
+class EdgeTests extends FunSuite:
+
+  test("should represent an edge with two vertexes") {
+    val v1    = Vertex.Zero
+    val v2    = Vertex(1)
+    val v3    = Vertex(3)
+    val edge1 = Edge(v1, v2)
+    val edge2 = Edge(v1 -> v2)
+    val edge3 = new Edge(v3, v1)
+    assertEquals(edge1, edge2)
+    assertNotEquals(edge1, edge3)
+    assertEquals(edge1.toString(), s"($v1, $v2)")
+    assertEquals(edge1.toString(), edge2.toString())
+    assertEquals(edge1.hashCode(), edge2.hashCode())
+    assertNotEquals(edge1.toString(), edge3.toString())
+    assertNotEquals(edge1.hashCode(), edge3.hashCode())
+    assertEquals(edge1.from, v1)
+    assertEquals(edge1.to, v2)
+    assertEquals(edge1.equals("unrelated-type"), false)
+  }
diff --git a/modules/core/src/test/scala/gs/graph/v0/SizeTests.scala b/modules/core/src/test/scala/gs/graph/v0/SizeTests.scala
new file mode 100644
index 0000000..981ff85
--- /dev/null
+++ b/modules/core/src/test/scala/gs/graph/v0/SizeTests.scala
@@ -0,0 +1,53 @@
+package gs.graph.v0
+
+import munit.*
+import scala.util.Try
+
+class SizeTests extends FunSuite:
+
+  test("should represent a vertex - some integer >= 0") {
+    val s1 = Size.Zero
+    val s2 = Size(0)
+    val s3 = Size(3)
+    assertEquals(s1, s2)
+    assertNotEquals(s1, s3)
+    assertEquals(s1.compare(s2), 0)
+    assertEquals(s1.compare(s3), -3)
+    assertEquals(s1.equals("unrelated-type"), false)
+    assertEquals(s1.hashCode(), s2.hashCode())
+    assertNotEquals(s1.hashCode(), s3.hashCode())
+    assertEquals(s1 < s3, true)
+    assertEquals(s1 < s2, false)
+    assertEquals(s1 > s3, false)
+    assertEquals(s3 > s1, true)
+    assertEquals(s1 < 3, true)
+    assertEquals(s1 < 0, false)
+    assertEquals(s1 > 0, false)
+    assertEquals(s3 > 0, true)
+    assertEquals(s1 < Vertex(3), true)
+    assertEquals(s1 < Vertex.Zero, false)
+    assertEquals(s1 > Vertex.Zero, false)
+    assertEquals(s3 > Vertex.Zero, true)
+    assertEquals(s1.toString(), s2.toString())
+    assertNotEquals(s1.toString(), s3.toString())
+    assertEquals(Size.Zero.value, 0)
+    assertEquals(Size.One.value, 1)
+  }
+
+  test("should throw an exception if an invalid value is given") {
+    Try(Size(-1)).toEither.left.toOption match
+      case None        => fail("Size instantiation should have failed.")
+      case Some(cause) =>
+        assertEquals(cause.getMessage(), "Size values must be 0 or greater.")
+  }
+
+  test("should instantiate from arrays based on the array length") {
+    val n1 = 3
+    val n2 = 5
+    val a1 = Array.fill(n1)(0)
+    val a2 = Array.fill(n2)(0)
+    val s1 = Size.fromArray(a1)
+    val s2 = Size.fromArray(a2)
+    assertEquals(s1.value, n1)
+    assertEquals(s2.value, n2)
+  }
diff --git a/modules/core/src/test/scala/gs/graph/v0/UndirectedGraphTests.scala b/modules/core/src/test/scala/gs/graph/v0/UndirectedGraphTests.scala
new file mode 100644
index 0000000..dda6fdb
--- /dev/null
+++ b/modules/core/src/test/scala/gs/graph/v0/UndirectedGraphTests.scala
@@ -0,0 +1,19 @@
+package gs.graph.v0
+
+import munit.*
+
+class UndirectedGraphTests extends FunSuite:
+
+  test("should support an empty graph") {
+    val g = UndirectedGraph.Empty
+    assertEquals(g.numberOfVertices, Size.Zero)
+    assertEquals(g.adjacency, Adjacency.Empty)
+    assertEquals(g.disposition, GraphDisposition.Undirected)
+    assertEquals(g.selectRoots(), Vector.empty)
+  }
+
+  test(
+    "should calculate roots based on an arbitrary vertex from each connected component"
+  ) {
+    // TODO: implement - current logic is wrong.
+  }
diff --git a/modules/core/src/test/scala/gs/graph/v0/VertexTests.scala b/modules/core/src/test/scala/gs/graph/v0/VertexTests.scala
new file mode 100644
index 0000000..305d2d0
--- /dev/null
+++ b/modules/core/src/test/scala/gs/graph/v0/VertexTests.scala
@@ -0,0 +1,40 @@
+package gs.graph.v0
+
+import munit.*
+import scala.util.Try
+
+class VertexTests extends FunSuite:
+
+  test("should represent a vertex - some integer >= 0") {
+    val v1 = Vertex.Zero
+    val v2 = Vertex(0)
+    val v3 = Vertex(3)
+    assertEquals(v1, v2)
+    assertNotEquals(v1, v3)
+    assertEquals(v1.compare(v2), 0)
+    assertEquals(v1.compare(v3), -3)
+    assertEquals(v1.equals("unrelated-type"), false)
+    assertEquals(v1.hashCode(), v2.hashCode())
+    assertNotEquals(v1.hashCode(), v3.hashCode())
+    assertEquals(v1 < v3, true)
+    assertEquals(v1 < v2, false)
+    assertEquals(v1 > v3, false)
+    assertEquals(v3 > v1, true)
+    assertEquals(v1 < 3, true)
+    assertEquals(v1 < 0, false)
+    assertEquals(v1 > 0, false)
+    assertEquals(v3 > 0, true)
+    assertEquals(v1 < Size(3), true)
+    assertEquals(v1 < Size.Zero, false)
+    assertEquals(v1 > Size.Zero, false)
+    assertEquals(v3 > Size.Zero, true)
+    assertEquals(v1.toString(), v2.toString())
+    assertNotEquals(v1.toString(), v3.toString())
+  }
+
+  test("should throw an exception if an invalid value is given") {
+    Try(Vertex(-1)).toEither.left.toOption match
+      case None        => fail("Vertex instantiation should have failed.")
+      case Some(cause) =>
+        assertEquals(cause.getMessage(), "Vertex values must be 0 or greater.")
+  }