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

@@ -93,12 +93,16 @@ sealed trait Adjacency:
   override def equals(that: Any): Boolean =
     val tuple = (this, that)
     tuple match
+      // Optimize when two default implementations are present.
       case (me: DefaultAdjacency, other: DefaultAdjacency) =>
         me.neighbors.length == other.neighbors.length
         && me.neighbors
           .zip(other.neighbors)
           .map { case (x, y) => x.sameElements(y) }
           .forall(result => result)
+      // Any two adjcency lists.
+      case (me: Adjacency, other: Adjacency) =>
+        me.entries.equals(other.entries)
       case _ => false
 
 object Adjacency:
@@ -136,6 +140,15 @@ object Adjacency:
     */
   final val Single: Adjacency = DefaultAdjacency.Single
 
+  /** Instantiate a single-vertex adjacency list.
+    *
+    * @param vertex
+    *   The vertex.
+    * @return
+    *   The new [[Adjacency]].
+    */
+  def single(vertex: Vertex): Adjacency = MappedAdjacency.single(vertex)
+
   /** Calculate an [[Adjacency]] from some collection of [[Edge]].
     *
     * @param numberOfVertices
@@ -152,6 +165,13 @@ object Adjacency:
     DefaultAdjacency.fromEdges(numberOfVertices, edges)
 
   /** Calculate an [[Adjacency]] from some collection of [[Edge]].
+    *
+    * This function uses the maximum vertex value as an upper bound and assumes
+    * that there are vertices with no neighbors within that bound -- it creates
+    * some [[DefaultAdjacency]].
+    *
+    * Used the mapped version if you want to ensure that _only_ the vertices
+    * referenced are contained in the result.
     *
     * @param edges
     *   The collection of [[Edge]] present in this graph.
@@ -163,6 +183,18 @@ object Adjacency:
   ): Adjacency =
     DefaultAdjacency.fromEdges(edges)
 
+  /** Calculate an [[Adjacency]] from some collection of [[Edge]].
+    *
+    * @param edges
+    *   The collection of [[Edge]] present in this graph.
+    * @return
+    *   The calculated [[Adjacency]].
+    */
+  def fromEdgesMapped(
+    edges: Iterable[Edge]
+  ): Adjacency =
+    MappedAdjacency.fromEdges(edges)
+
 end Adjacency
 
 /** An immutable adjacency list representation.

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

@@ -4,11 +4,12 @@ import gs.graph.v0.Vertex
 import scala.collection.mutable.ListBuffer
 import scala.collection.mutable.Queue
 
-/** Represents a _ Connected Component_.
+/** Represents a _Connected Component_.
-  *
-  * TODO: ADD EDGES!
   */
-final class ConnectedComponent private (val value: Set[Vertex]):
+final class ConnectedComponent private (
+  val value: Set[Vertex],
+  val adjacency: Adjacency
+):
 
   /** @inheritDocs
     */
@@ -25,9 +26,13 @@ final class ConnectedComponent private (val value: Set[Vertex]):
     */
   override def toString(): String =
     val sb = StringBuilder()
-    sb.append("[")
+    sb.append("entries:[\n")
-    sb.append(value.mkString(","))
+    sb.append(
-    sb.append("]")
+      adjacency.entries
+        .map { case (v, ns) => s"$v -> ${ns.mkString(",")}" }
+        .mkString("\n")
+    )
+    sb.append("\n]")
     sb.toString()
 
   /** @return
@@ -53,30 +58,6 @@ end ConnectedComponent
 
 object ConnectedComponent:
 
-  /** Instantiate a new Connected Component from the given collection of
-    * [[Vertex]].
-    *
-    * This constructor ensures that each [[Vertex]] only occurs once.
-    *
-    * @param value
-    *   The input collection.
-    * @return
-    *   The new Connected Component.
-    */
-  def apply(value: Vertex*): ConnectedComponent =
-    if value.isEmpty then
-      throw new IllegalArgumentException(
-        "Empty connected components are not allowed."
-      )
-    else new ConnectedComponent(value.toSet)
-
-  def of(value: Int*): ConnectedComponent =
-    if value.isEmpty then
-      throw new IllegalArgumentException(
-        "Empty connected components are not allowed."
-      )
-    else new ConnectedComponent(value.map(Vertex.apply).toSet)
-
   /** Instantiate a new Connected Component that contains a single [[Vertex]].
     *
     * @param value
@@ -85,7 +66,7 @@ object ConnectedComponent:
     *   The new Connected Component.
     */
   def single(value: Vertex): ConnectedComponent =
-    new ConnectedComponent(Set(value))
+    new ConnectedComponent(Set(value), Adjacency.single(value))
 
   given CanEqual[ConnectedComponent, ConnectedComponent] = CanEqual.derived
 
@@ -120,7 +101,8 @@ object ConnectedComponent:
         else ()
       }
 
-    new ConnectedComponent(b.toSet)
+    val vs = b.toSet
+    new ConnectedComponent(vs, g.adjacency.subset(vs))
 
   private class Tracker(val data: Array[Boolean]):
     def visit(v: Vertex): Unit = data(v.ordinal) = true

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

@@ -22,7 +22,7 @@ class AdjacencyTests extends munit.FunSuite:
   private val adj = Adjacency.fromEdges(size, edges)
 
   test("should provide equality") {
-    val a2 = Adjacency(adj.neighbors)
+    val a2 = MappedAdjacency.validate(adj.entries)
     val a3 = Adjacency.Single
 
     assertEquals(adj, a2)

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

@@ -37,20 +37,3 @@ class UndirectedGraphTests extends FunSuite:
     assertEquals(g.neighbors(Vertex(0)), Vector(Vertex(1), Vertex(2)))
     assertEquals(g.neighbors(Vertex(4)), Vector.empty)
   }
-
-  test("should calculate roots for each connected component") {
-    val N = Size(10)
-    val g = Graph.undirected(
-      numberOfVertices = N,
-      edges = 0 -> 1,
-      1 -> 2,
-      2 -> 3,
-      4 -> 5,
-      5 -> 6,
-      4 -> 6,
-      7 -> 8
-    )
-    val expectedRoots = Vertex.of(0, 4, 7, 9)
-
-    assertEquals(g.roots, expectedRoots)
-  }

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

@@ -11,7 +11,6 @@ class DigraphTests extends FunSuite:
     val dg = Digraph.Empty
     assertEquals(dg.numberOfVertices, Size.Zero)
     assertEquals(dg.isSingle, false)
-    assertEquals(dg.roots, Vector.empty)
     assertEquals(dg.isEmpty, true)
     assertEquals(dg.neighbors(Vertex.Zero), Vector.empty)
     assertEquals(dg.hasCycle, false)
@@ -21,7 +20,6 @@ class DigraphTests extends FunSuite:
     val dg = Digraph.Single
     assertEquals(dg.numberOfVertices, Size.One)
     assertEquals(dg.isSingle, true)
-    assertEquals(dg.roots, Vertex.of(0))
     assertEquals(dg.isEmpty, false)
     assertEquals(dg.neighbors(Vertex.Zero), Vector.empty)
     assertEquals(dg.hasCycle, false)

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

@@ -5,6 +5,7 @@ import gs.graph.v0.Edge
 import gs.graph.v0.Graph
 import gs.graph.v0.Size
 import gs.graph.v0.Vertex
+import gs.graph.v0.syntax.V
 import munit.*
 
 class TarjansTests extends FunSuite:
@@ -13,13 +14,13 @@ class TarjansTests extends FunSuite:
     val v0 = Vertex.Zero
     val v1 = Vertex(1)
     val v2 = Vertex(2)
-    val s1 = StronglyConnectedComponent(v0)
+    val s1 = StronglyConnectedComponent.single(v0)
-    val s2 = StronglyConnectedComponent(v0, v1, v2)
+    val s2 = StronglyConnectedComponent.of(0 -> 1, 1 -> 2, 2 -> 0)
-    val s3 = StronglyConnectedComponent(v0)
+    val s3 = StronglyConnectedComponent.single(v0)
 
     assertEquals(s1, s3)
     assertNotEquals(s1, s2)
-    assertEquals(s2.value, Set(v0, v1, v2))
+    assertEquals(s2.vertices, Set(v0, v1, v2))
     assertEquals(s2.vertices, Set(v0, v1, v2))
     assertEquals(s2.size, 3)
     assertEquals(s2.isSingle, false)
@@ -60,13 +61,12 @@ class TarjansTests extends FunSuite:
     )
 
     val sccs = StronglyConnectedComponent.findAll(g)
-    assertEquals(g.roots, Vector(Vertex.Zero))
     assertEquals(
       sccs.toSet,
       Set(
-        StronglyConnectedComponent.of(0),
+        StronglyConnectedComponent.single(V(0)),
-        StronglyConnectedComponent.of(1),
+        StronglyConnectedComponent.single(V(1)),
-        StronglyConnectedComponent.of(2)
+        StronglyConnectedComponent.single(V(2))
       )
     )
   }
@@ -99,13 +99,12 @@ class TarjansTests extends FunSuite:
     )
 
     val sccs = StronglyConnectedComponent.findAll(g)
-    assertEquals(g.roots, Vector.empty)
     assertEquals(
       sccs.toSet,
       Set(
-        StronglyConnectedComponent.of(0, 1, 2),
+        StronglyConnectedComponent.of(0 -> 1, 1 -> 2, 2 -> 0),
-        StronglyConnectedComponent.of(3, 4, 5),
+        StronglyConnectedComponent.of(3 -> 4, 4 -> 5, 5 -> 3),
-        StronglyConnectedComponent.of(6, 7, 8)
+        StronglyConnectedComponent.of(6 -> 7, 7 -> 8, 8 -> 6)
       )
     )
   }