Some minor improvements to construction.

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]].
     *
@@ -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)
     val buffs = Vector.fill(numberOfVertices.value)(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

@@ -16,6 +16,8 @@ final class Edge private (
   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.
     *
@@ -103,4 +105,14 @@ object Edge:
     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/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

@@ -5,17 +5,17 @@ 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 E  = Edge.list(
+      0 -> 1,
+      0 -> 2,
+      0 -> 3,
+      1 -> 4,
+      2 -> 4,
+      3 -> 4,
+      3 -> 5,
+      4 -> 6
     )
-    val A = Adjacency.fromDirectedEdges(N, E)
+    val A = Adjacency.fromEdges(N, E)
 
     assertEquals(A.incoming(vs(0)), Vector.empty)
     assertEquals(A.incoming(vs(1)), Vector(vs(0)))

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

@@ -10,7 +10,7 @@ class EdgeTests extends FunSuite:
     val v3    = Vertex(3)
     val edge1 = Edge(v1, v2)
     val edge2 = Edge(v1 -> v2)
-    val edge3 = new Edge(v3, v1)
+    val edge3 = Edge(v3, v1)
     assertEquals(edge1, edge2)
     assertNotEquals(edge1, edge3)
     assertEquals(edge1.toString(), s"($v1, $v2)")

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
         )
       )
     )