(minor) coverage, fixes, updates

build.sbt

@@ -1,4 +1,4 @@
-val scala3: String = "3.8.2"
+val scala3: String = "3.8.3"
 
 ThisBuild / scalaVersion  := scala3
 ThisBuild / versionScheme := Some("semver-spec")
@@ -38,7 +38,7 @@ val Deps = new {
     val Datagen: ModuleID = "gs" %% "gs-datagen-core-v0" % "0.4.1"
   }
 
-  val MUnit: ModuleID = "org.scalameta" %% "munit" % "1.2.4"
+  val MUnit: ModuleID = "org.scalameta" %% "munit" % "1.3.0"
 }
 
 lazy val testSettings = Seq(

modules/core/src/main/scala/gs/graph/v0/Adjacency.scala

@@ -8,7 +8,7 @@ import scala.collection.mutable.ListBuffer
   * the corresponding vector is a "to" [[Vertex]] -- there are edges _from_ some
   * vertex _to_ another vertex.
   */
-final class Adjacency(val neighbors: Vector[Vector[Vertex]]):
+final class Adjacency private (val neighbors: Vector[Vector[Vertex]]):
   /** Get the vector of [[Vertex]] that receive a connection _from_ the input
     * [[Vertex]].
     *
@@ -103,7 +103,7 @@ object Adjacency:
     * @return
     *   Some new empty adjacency.
     */
-  def empty(numberOfVertices: Size): Adjacency =
+  def noEdges(numberOfVertices: Size): Adjacency =
     new Adjacency(Vector.fill(numberOfVertices.value)(Vector.empty))
 
   given CanEqual[Adjacency, Adjacency] = CanEqual.derived
@@ -118,8 +118,7 @@ object Adjacency:
     */
   final val Single: Adjacency = new Adjacency(Vector(Vector.empty))
 
-  /** Calculate an [[Adjacency]] from some collection of [[Edge]], where those
-    * edges are assumed to be directed.
+  /** Calculate an [[Adjacency]] from some collection of [[Edge]].
     *
     * @param numberOfVertices
     *   The number of [[Vertex]] (`N`) in this graph.
@@ -128,14 +127,44 @@ object Adjacency:
     * @return
     *   The calculated [[Adjacency]].
     */
-  def fromDirectedEdges(
+  def fromEdges(
     numberOfVertices: Size,
     edges: Iterable[Edge]
   ): Adjacency =
     val buffs = Vector.fill(numberOfVertices.value)(ListBuffer.empty[Vertex])
+    val _     = edges.foreach { edge =>
+      if edge.v1 >= numberOfVertices || edge.v2 >= numberOfVertices then
+        throw new IllegalArgumentException(
+          s"Edge (${edge.v1}, ${edge.v2}) is out of bounds. Maximum vertex value is ${numberOfVertices.value - 1}"
+        )
+      else
+        val _ = buffs(edge.from.ordinal).addOne(edge.to)
+    }
+    new Adjacency(buffs.map(_.distinct.toVector))
+
+  /** Calculate an [[Adjacency]] from some collection of [[Edge]].
+    *
+    * @param edges
+    *   The collection of [[Edge]] present in this graph.
+    * @return
+    *   The calculated [[Adjacency]].
+    */
+  def fromEdges(
+    edges: Iterable[Edge]
+  ): Adjacency =
+    val numberOfVertices = findMaximumVertex(edges).ordinal + 1
+    val buffs = Vector.fill(numberOfVertices)(ListBuffer.empty[Vertex])
     val _     = edges.foreach { edge =>
       val _ = buffs(edge.from.ordinal).addOne(edge.to)
     }
     new Adjacency(buffs.map(_.distinct.toVector))
 
+  private def findMaximumVertex(edges: Iterable[Edge]): Vertex =
+    var maximum = Vertex.Zero
+    edges.foreach { edge =>
+      if edge.max > maximum then maximum = edge.max
+      else ()
+    }
+    maximum
+
 end Adjacency

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`.
   *
@@ -11,11 +11,13 @@ import java.util.Objects
   * @param v2
   *   The second [[Vertex]].
   */
-final class Edge(
+final class Edge private (
   val v1: Vertex,
   val v2: Vertex
 ):
 
+  def max: Vertex = if v1 >= v2 then v1 else v2
+
   /** When considering this edge as _directed_, this function returns the
     * [[Vertex]] that is the beginning of the connection.
     *
@@ -54,11 +56,63 @@ 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))
+
+  /** Instantiate a list of Edge.
+    *
+    * @param edges
+    *   The list of Edge.
+    * @return
+    *   The captured list of Edge.
+    */
+  def list(edges: (Int, Int)*): List[Edge] =
+    edges.map(e => apply(e._1, e._2)).toList
 
 end Edge

modules/core/src/main/scala/gs/graph/v0/Graph.scala

@@ -58,3 +58,41 @@ trait Graph:
       case _ => false
 
 end Graph
+
+object Graph:
+
+  /** Construct a new [[UndirectedGraph]] from the given [[Edge]].
+    *
+    * @param numberOfVertices
+    *   The number of vertices in this [[Graph]].
+    * @param edges
+    *   The [[Edge]] in this graph.
+    * @return
+    *   The new [[UndirectedGraph]].
+    */
+  def undirected(
+    numberOfVertices: Size,
+    edges: (Int, Int)*
+  ): UndirectedGraph =
+    new UndirectedGraph(
+      numberOfVertices,
+      Adjacency.fromEdges(numberOfVertices, Edge.list(edges*))
+    )
+
+  /** Construct a new [[UndirectedGraph]] from the given [[Edge]].
+    *
+    * @param edges
+    *   The [[Edge]] in this graph.
+    * @return
+    *   The new [[UndirectedGraph]].
+    */
+  def undirected(
+    edges: (Int, Int)*
+  ): UndirectedGraph =
+    val adj = Adjacency.fromEdges(Edge.list(edges*))
+    new UndirectedGraph(
+      adj.numberOfVertices,
+      adj
+    )
+
+end Graph

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
@@ -6,8 +6,51 @@ import scala.collection.mutable.ListBuffer
 import scala.collection.mutable.Stack
 
 /** Represents a _Strongly Connected Component_ (SCC).
+  *
+  * Each SCC is guaranteed to be non-empty.
   */
-opaque type SCC = Vector[Vertex]
+final class SCC private (val value: Set[Vertex]):
+
+  /** @inheritDocs
+    */
+  override def equals(obj: Any): Boolean =
+    obj match
+      case other: SCC => value.equals(other.value)
+      case _          => false
+
+  /** @inheritDocs
+    */
+  override def hashCode(): Int = value.hashCode()
+
+  /** @inheritDocs
+    */
+  override def toString(): String =
+    val sb = StringBuilder()
+    sb.append("[")
+    sb.append(value.mkString(","))
+    sb.append("]")
+    sb.toString()
+
+  /** @return
+    *   The number of vertices contained by this SCC.
+    */
+  def size: Int = value.size
+
+  /** @return
+    *   True if this SCC contains a single vertex.
+    */
+  def isSingle: Boolean = value.size == 1
+
+  /** @return
+    *   The set of vertices in the SCC.
+    */
+  def vertices: Set[Vertex] = value
+
+  /** Retrieve an arbitrary SCC member as the root vertex.
+    */
+  lazy val root: Vertex = value.toList.head
+
+end SCC
 
 object SCC:
 
@@ -20,36 +63,54 @@ object SCC:
     * @return
     *   The new SCC.
     */
-  def apply(value: Seq[Vertex]): SCC = value.distinct.toVector
+  def apply(value: Vertex*): SCC =
+    if value.isEmpty then
+      throw new IllegalArgumentException(
+        "Empty strongly connected components (SCC) are not allowed."
+      )
+    else new SCC(value.toSet)
+
+  def of(value: Int*): SCC =
+    if value.isEmpty then
+      throw new IllegalArgumentException(
+        "Empty strongly connected components (SCC) are not allowed."
+      )
+    else new SCC(value.map(Vertex.apply).toSet)
+
+  /** Instantiate a new SCC that contains a single [[Vertex]].
+    *
+    * @param value
+    *   The input vertex.
+    * @return
+    *   The new SCC.
+    */
+  def single(value: Vertex): SCC = new SCC(Set(value))
 
   given CanEqual[SCC, SCC] = CanEqual.derived
 
-  extension (scc: SCC)
-    /** @return
-      *   The underlying value of this SCC.
-      */
-    def unwrap(): Vector[Vertex] = scc
-
-    /** @return
-      *   The vertices contained by this SCC.
-      */
-    def vertices: Vector[Vertex] = scc
-
-    /** @return
-      *   The number of vertices contained by this SCC.
-      */
-    def size: Int = scc.size
-
-    /** @return
-      *   True if this SCC contains a single vertex.
-      */
-    def isSingle: Boolean = scc.size == 1
-
-  /** Implementation of Tarjan's Algorithm for finding all strongly connected
-    * components for some directed graph.
+  /** Alias for `findAll`.
+    *
+    * Implementation of Tarjan's Algorithm for finding all strongly connected
+    * components for some graph.
+    *
+    * This algorithm captures directed cycles. Any vertex not part of some
+    * directed cycle (e.g. every node in a DAG) forms an SCC by itself.
     *
     * @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.
+    *
+    * This algorithm captures directed cycles. Any vertex not part of some
+    * directed cycle (e.g. every node in a DAG) forms an SCC by itself.
+    *
+    * @param g
+    *   The graph to analyze.
     * @return
     *   The complete list of [[SCC]] for the input graph.
     */
@@ -134,14 +195,22 @@ object SCC:
         sccVertex = s.pop()
 
       scc.addOne(sccVertex)
-      output.addOne(SCC(scc.toVector))
+      if !scc.isEmpty then output.addOne(new SCC(scc.toSet))
+      else println("ERROR")
     else ()
 
-  final private class Counter(var i: Int = 0):
+  /** Mutable state wrapper around an integer.
+    *
+    * @param i
+    *   The integer value.
+    */
+  final private class Counter(var i: Int):
 
     def increment(): Unit =
       i += 1
 
     def get(): Int = i
 
+  end Counter
+
 end SCC

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 +101,24 @@ object Size:
     */
   def fromVector(vec: Vector[?]): Size = new Size(vec.length)
 
+  /** Instantiate the size of any iterable.
+    *
+    * @param iter
+    *   The iterable.
+    * @return
+    *   Size representing the total length of the iterable.
+    */
+  def of(iter: Iterable[?]): Size = new Size(iter.size)
+
+  given CanEqual[Size, Size] = CanEqual.derived
+
+  given Ordering[Size] with
+
+    /** @inheritDocs
+      */
+    def compare(
+      x: Size,
+      y: Size
+    ): Int = x.value - y.value
+
 end Size

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(_.root)
 
 end UndirectedGraph
 

modules/core/src/main/scala/gs/graph/v0/Vertex.scala

@@ -8,6 +8,11 @@ package gs.graph.v0
   */
 final class Vertex private (val ordinal: Int) extends Ordered[Vertex]:
 
+  /** @return
+    *   The value (ordinal) of the Vertex.
+    */
+  def value: Int = ordinal
+
   /** @inheritDocs
     */
   override def compare(that: Vertex): Int =
@@ -37,6 +42,16 @@ final class Vertex private (val ordinal: Int) extends Ordered[Vertex]:
     */
   infix def <(value: Int): Boolean = ordinal < value
 
+  /** Is the ordinal of this vertex less than or equal to some integer value?
+    *
+    * @param value
+    *   The integer value.
+    * @return
+    *   True if the ordinal is less than or equal to the integer value. False
+    *   otherwise.
+    */
+  infix def <=(value: Int): Boolean = ordinal <= value
+
   /** Is the ordinal of this vertex greater than some integer value?
     *
     * @param value
@@ -46,6 +61,16 @@ final class Vertex private (val ordinal: Int) extends Ordered[Vertex]:
     */
   infix def >(value: Int): Boolean = ordinal > value
 
+  /** Is the ordinal of this vertex greater than or equal to some integer value?
+    *
+    * @param value
+    *   The integer value.
+    * @return
+    *   True if the ordinal is greater than or equal to the integer value. False
+    *   otherwise.
+    */
+  infix def >=(value: Int): Boolean = ordinal >= value
+
   /** Is the ordinal of this vertex less than some [[Size]] value?
     *
     * @param value
@@ -55,6 +80,16 @@ final class Vertex private (val ordinal: Int) extends Ordered[Vertex]:
     */
   infix def <(size: Size): Boolean = ordinal < size.value
 
+  /** Is the ordinal of this vertex less than or equal to some [[Size]] value?
+    *
+    * @param value
+    *   The [[Size]] value.
+    * @return
+    *   True if the ordinal is less than or equal to the [[Size]] value. False
+    *   otherwise.
+    */
+  infix def <=(size: Size): Boolean = ordinal <= size.value
+
   /** Is the ordinal of this vertex greater than some [[Size]] value?
     *
     * @param value
@@ -64,6 +99,17 @@ final class Vertex private (val ordinal: Int) extends Ordered[Vertex]:
     */
   infix def >(size: Size): Boolean = ordinal > size.value
 
+  /** Is the ordinal of this vertex greater than or equal to some [[Size]]
+    * value?
+    *
+    * @param value
+    *   The [[Size]] value.
+    * @return
+    *   True if the ordinal is greater than or equal to the [[Size]] value.
+    *   False otherwise.
+    */
+  infix def >=(size: Size): Boolean = ordinal >= size.value
+
 object Vertex:
 
   /** The fixed value 0 expressed as a [[Vertex]].

modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala

@@ -63,7 +63,7 @@ object Digraph:
   ): Digraph =
     new Digraph(
       numberOfVertices = numberOfVertices,
-      adjacency = Adjacency.fromDirectedEdges(numberOfVertices, edges),
+      adjacency = Adjacency.fromEdges(numberOfVertices, edges),
       roots = findRootsForDirectedEdges(numberOfVertices, edges)
     )
 

modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDigraph.scala

@@ -61,7 +61,7 @@ object SingleRootDigraph:
     if root < numberOfVertices then
       new SingleRootDigraph(
         numberOfVertices,
-        Adjacency.fromDirectedEdges(numberOfVertices, edges),
+        Adjacency.fromEdges(numberOfVertices, edges),
         root
       )
     else throw GraphException.RootOutOfBounds(root, numberOfVertices)
@@ -86,7 +86,7 @@ object SingleRootDigraph:
       Some(
         new SingleRootDigraph(
           numberOfVertices,
-          Adjacency.fromDirectedEdges(numberOfVertices, edges),
+          Adjacency.fromEdges(numberOfVertices, edges),
           roots(0)
         )
       )

modules/core/src/test/scala/gs/graph/v0/AdjacencyTests.scala

@@ -1,27 +1,91 @@
 package gs.graph.v0
 
+import scala.util.Failure
+import scala.util.Try
+
 class AdjacencyTests extends munit.FunSuite:
 
-  test("should provide incoming connections") {
-    val N  = Size(7)
-    val vs = (0 until N.value).map(Vertex(_)).toArray
-    val E  = List(
-      Edge(vs(0), vs(1)),
-      Edge(vs(0), vs(2)),
-      Edge(vs(0), vs(3)),
-      Edge(vs(1), vs(4)),
-      Edge(vs(2), vs(4)),
-      Edge(vs(3), vs(4)),
-      Edge(vs(3), vs(5)),
-      Edge(vs(4), vs(6))
-    )
-    val A = Adjacency.fromDirectedEdges(N, E)
+  private val size = Size(7)
+  private val vs   = (0 until size.value).map(Vertex(_)).toArray
 
-    assertEquals(A.incoming(vs(0)), Vector.empty)
-    assertEquals(A.incoming(vs(1)), Vector(vs(0)))
-    assertEquals(A.incoming(vs(2)), Vector(vs(0)))
-    assertEquals(A.incoming(vs(3)), Vector(vs(0)))
-    assertEquals(A.incoming(vs(4)), Vector(vs(1), vs(2), vs(3)))
-    assertEquals(A.incoming(vs(5)), Vector(vs(3)))
-    assertEquals(A.incoming(vs(6)), Vector(vs(4)))
+  private val edges = Edge.list(
+    0 -> 1,
+    0 -> 2,
+    0 -> 3,
+    1 -> 4,
+    2 -> 4,
+    3 -> 4,
+    3 -> 5,
+    4 -> 6
+  )
+
+  private val adj = Adjacency.fromEdges(size, edges)
+
+  test("should provide equality") {
+    val a2 = Adjacency(adj.neighbors)
+    val a3 = Adjacency.Single
+
+    assertEquals(adj, a2)
+    assertNotEquals(adj, a3)
+    assert(!adj.equals(null))
+    assert(!adj.equals("anything"))
+  }
+
+  test("should provide incoming connections") {
+    assertEquals(adj.incoming(vs(0)), Vector.empty)
+    assertEquals(adj.incoming(vs(1)), Vector(vs(0)))
+    assertEquals(adj.incoming(vs(2)), Vector(vs(0)))
+    assertEquals(adj.incoming(vs(3)), Vector(vs(0)))
+    assertEquals(adj.incoming(vs(4)), Vector(vs(1), vs(2), vs(3)))
+    assertEquals(adj.incoming(vs(5)), Vector(vs(3)))
+    assertEquals(adj.incoming(vs(6)), Vector(vs(4)))
+  }
+
+  test("should show no incoming connections for a vertex not in the graph") {
+    assertEquals(adj.incoming(Vertex(999)), Vector.empty)
+  }
+
+  test("should express an adjacency as edges") {
+    val es = adj.toEdges()
+    assertEquals(es, edges.toVector)
+  }
+
+  test("should track the number of vertices in the graph") {
+    assertEquals(adj.numberOfVertices, size)
+  }
+
+  test("should track the number of edges in the graph") {
+    assertEquals(adj.numberOfEdges, Size.of(edges))
+  }
+
+  test("should construct an adjacency with no edges") {
+    val sz = Size(10)
+    val a  = Adjacency.noEdges(sz)
+    assertEquals(a.numberOfVertices, sz)
+    assertEquals(a.numberOfEdges, Size.Zero)
+  }
+
+  test(
+    "should guard against out of bound values when building from edges with an explicit bound"
+  ) {
+    val n  = Size(2)
+    val es = Edge.list(0 -> 3)
+    Try(Adjacency.fromEdges(n, es)) match
+      case Failure(ex: IllegalArgumentException) =>
+        assertEquals(
+          ex.getMessage(),
+          "Edge (0, 3) is out of bounds. Maximum vertex value is 1"
+        )
+      case _ =>
+        fail(
+          "Expected adjacency construction to fail with an IllegalArgumentException."
+        )
+  }
+
+  test("should construct from edges, finding the largest known vertex") {
+    val expectedSize = Size(10)
+    val es           = Edge.list(0 -> 1, 1 -> 2, 0 -> 9, 3 -> 1)
+    val a            = Adjacency.fromEdges(es)
+    assertEquals(a.numberOfVertices, expectedSize)
+    assertEquals(a.numberOfEdges, Size.of(es))
   }

modules/core/src/test/scala/gs/graph/v0/EdgeTests.scala

@@ -0,0 +1,36 @@
+package gs.graph.v0
+
+import munit.*
+import scala.util.Failure
+import scala.util.Try
+
+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 = 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)
+  }
+
+  test("should forbid loop edges") {
+    Try(Edge(1, 1)) match
+      case Failure(ex: IllegalArgumentException) =>
+        assertEquals(
+          ex.getMessage(),
+          "Loop edges are not supported. Edges must refer to two distinct vertexes."
+        )
+      case _ => fail("Expected to fail with an IllegalArgumentException")
+  }

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)
+  }

modules/core/src/test/scala/gs/graph/v0/TarjansTests.scala

@@ -0,0 +1,102 @@
+package gs.graph.v0
+
+import gs.graph.v0.directed.Digraph
+import munit.*
+
+class TarjansTests extends FunSuite:
+
+  test("should provide basic SCC representation") {
+    val v0 = Vertex.Zero
+    val v1 = Vertex(1)
+    val v2 = Vertex(2)
+    val s1 = SCC(v0)
+    val s2 = SCC(v0, v1, v2)
+    val s3 = SCC(v0)
+
+    assertEquals(s1, s3)
+    assertNotEquals(s1, s2)
+    assertEquals(s2.value, Set(v0, v1, v2))
+    assertEquals(s2.vertices, Set(v0, v1, v2))
+    assertEquals(s2.size, 3)
+    assertEquals(s2.isSingle, false)
+    assertEquals(s1.isSingle, true)
+  }
+
+  test("should produce an empty list of SCCs for an empty graph") {
+    val g    = UndirectedGraph.Empty
+    val sccs = SCC.tarjan(g)
+    val alt  = SCC.findAll(g)
+    assertEquals(sccs, Nil)
+    assertEquals(alt, Nil)
+  }
+
+  test(
+    "should produce a list of once SCC with one vertex for a graph with one vertex"
+  ) {
+    val g        = Graph.undirected(Size.One)
+    val sccs     = SCC.findAll(g)
+    val expected = SCC.single(Vertex.Zero)
+    assertEquals(sccs, List(expected))
+  }
+
+  /** Each vertex of a DAG is an SCC.
+    */
+  test("should identify a single SCC for a single 'line' of vertices") {
+    val n = Size(3)
+
+    // 0 -> 1 -> 2
+    val g = Digraph.fromAdjacency(
+      Adjacency.fromEdges(
+        n,
+        List(
+          Edge(0, 1),
+          Edge(1, 2)
+        )
+      )
+    )
+
+    val sccs = SCC.findAll(g)
+    assertEquals(g.roots, Vector(Vertex.Zero))
+    assertEquals(sccs.toSet, Set(SCC.of(0), SCC.of(1), SCC.of(2)))
+  }
+
+  test("should handle a graph with multiple SCCs") {
+    val n = Size(9)
+
+    // Establish discrete cycles
+    // 0 -> 1 -> 2 -> 0
+    // 3 -> 4 -> 5 -> 3
+    // 6 -> 7 -> 8 -> 6
+    val g = Digraph.fromAdjacency(
+      Adjacency.fromEdges(
+        n,
+        List(
+          // Cycle 1
+          Edge(0, 1),
+          Edge(1, 2),
+          Edge(2, 0),
+          // Cycle 2
+          Edge(3, 4),
+          Edge(4, 5),
+          Edge(5, 3),
+          // Cycle 3
+          Edge(6, 7),
+          Edge(7, 8),
+          Edge(8, 6)
+        )
+      )
+    )
+
+    val sccs = SCC.findAll(g)
+    assertEquals(g.roots, Vector.empty)
+    assertEquals(
+      sccs.toSet,
+      Set(
+        SCC.of(0, 1, 2),
+        SCC.of(3, 4, 5),
+        SCC.of(6, 7, 8)
+      )
+    )
+  }
+
+end TarjansTests

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.
+  }

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.")
+  }

modules/core/src/test/scala/gs/graph/v0/directed/DagTests.scala

@@ -3,7 +3,6 @@ package gs.graph.v0.directed
 import gs.graph.v0.Adjacency
 import gs.graph.v0.Edge
 import gs.graph.v0.Size
-import gs.graph.v0.Vertex
 import munit.*
 
 class DagTests extends FunSuite:
@@ -23,20 +22,19 @@ class DagTests extends FunSuite:
 
   test("should validate a single-root graph") {
     val size             = Size(8)
-    val vs               = (0 until size.value).map(Vertex(_))
     val digraph: Digraph = Digraph.fromAdjacency(
-      Adjacency.fromDirectedEdges(
+      Adjacency.fromEdges(
         numberOfVertices = size,
-        edges = Seq(
-          Edge(vs(0) -> vs(1)),
-          Edge(vs(0) -> vs(2)),
-          Edge(vs(0) -> vs(3)),
-          Edge(vs(1) -> vs(4)),
-          Edge(vs(2) -> vs(4)),
-          Edge(vs(3) -> vs(5)),
-          Edge(vs(4) -> vs(6)),
-          Edge(vs(5) -> vs(6)),
-          Edge(vs(6) -> vs(7))
+        edges = Edge.list(
+          0 -> 1,
+          0 -> 2,
+          0 -> 3,
+          1 -> 4,
+          2 -> 4,
+          3 -> 5,
+          4 -> 6,
+          5 -> 6,
+          6 -> 7
         )
       )
     )
@@ -48,15 +46,14 @@ class DagTests extends FunSuite:
 
   test("should NOT validate a single-root digraph with a cycle") {
     val size             = Size(4)
-    val vs               = (0 until size.value).map(Vertex(_))
     val digraph: Digraph = Digraph.fromAdjacency(
-      Adjacency.fromDirectedEdges(
+      Adjacency.fromEdges(
         numberOfVertices = size,
-        edges = Seq(
-          Edge(vs(0) -> vs(1)),
-          Edge(vs(1) -> vs(2)),
-          Edge(vs(2) -> vs(3)),
-          Edge(vs(3) -> vs(1))
+        edges = Edge.list(
+          0 -> 1,
+          1 -> 2,
+          2 -> 3,
+          3 -> 1
         )
       )
     )

project/build.properties

@@ -1 +1 @@
-sbt.version=1.12.8
+sbt.version=1.12.11