WIP: More fixes and traversal fully tested for non-enriched graphs.

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

@@ -1,6 +1,7 @@
 package gs.graph.v0
 
 import gs.graph.v0.directed.Digraph
+import scala.collection.IndexedSeqView
 
 /** Graph representation based on an adjacency list.
   *
@@ -29,6 +30,12 @@ trait Graph:
     */
   def numberOfVertices: Size
 
+  /** @return
+    *   View over all [[Vertex]] values in this graph.
+    */
+  def view: IndexedSeqView[Vertex] =
+    (0 until numberOfVertices.value).view.map(Vertex(_))
+
   /** @return
     *   True if this graph has no vertices, false otherwise.
     */

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

@@ -7,13 +7,19 @@ package gs.graph.v0
   */
 sealed abstract class GraphDisposition(val name: String):
 
+  /** @inheritDocs
+    */
   override def equals(that: Any): Boolean =
     that match
       case other: GraphDisposition => name == other.name
       case _                       => false
 
+  /** @inheritDocs
+    */
   override def hashCode(): Int = name.hashCode()
 
+  /** @inheritDocs
+    */
   override def toString(): String = name
 
 object GraphDisposition:
@@ -28,4 +34,17 @@ object GraphDisposition:
     */
   case object Undirected extends GraphDisposition("undirected")
 
+  /** Parse the given string as a [[GraphDisposition]].
+    *
+    * @param candidate
+    *   The string to validate.
+    * @return
+    *   The parsed [[GraphDisposition]], or `None` if the input does not
+    *   represent a valid disposition.
+    */
+  def parse(candidate: String): Option[GraphDisposition] =
+    if candidate.equalsIgnoreCase(Directed.name) then Some(Directed)
+    else if candidate.equalsIgnoreCase(Undirected.name) then Some(Undirected)
+    else None
+
 end GraphDisposition

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

@@ -12,9 +12,6 @@ object GraphTraversal:
   /** Depth-first search that executes a side-effecting function on each
     * [[Vertex]]. This function will operate on _any_ [[Graph]].
     *
-    * This implementation selects the first [[Vertex]] as an arbitrary starting
-    * point.
-    *
     * @param graph
     *   The input [[Graph]] on which to run DFS.
     * @param visit
@@ -27,7 +24,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    graph.selectRoots().foreach { root =>
+    graph.view.foreach { root =>
+      if !discovered(root.ordinal) then
         val _ = s.push(root)
         while !s.isEmpty
         do
@@ -35,17 +33,14 @@ object GraphTraversal:
           if !discovered(v.ordinal) then
             val _ = visit(v)
             discovered(v.ordinal) = true
-          graph.neighbors(v).foreach(w => s.push(w))
+            val _ = graph.neighbors(v).reverseIterator.foreach(s.push)
+          else ()
       else ()
-      ()
     }
 
   /** Depth-first search that executes a function on each [[Vertex]] to produce
     * some output. This function will operate on _any_ [[Graph]].
     *
-    * This implementation selects the first [[Vertex]] as an arbitrary starting
-    * point.
-    *
     * @param graph
     *   The input [[Graph]] on which to run DFS.
     * @param visit
@@ -61,7 +56,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    graph.selectRoots().foreach { root =>
+    graph.view.foreach { root =>
+      if !discovered(root.ordinal) then
         val _ = s.push(root)
         while !s.isEmpty
         do
@@ -69,12 +65,26 @@ object GraphTraversal:
           if !discovered(v.ordinal) then
             val _ = output.addOne(visit(v))
             discovered(v.ordinal) = true
-          graph.neighbors(v).foreach(w => s.push(w))
+            val _ = graph.neighbors(v).reverseIterator.foreach(s.push)
+          else ()
       else ()
     }
 
     output.toList
 
+  /** Depth-first search that executes a function on each [[Vertex]] in the
+    * context of some accumulator value to produce some accumulated output. This
+    * function will operate on _any_ [[Graph]].
+    *
+    * @param graph
+    *   The input [[Graph]] on which to run DFS.
+    * @param initial
+    *   The initial value.
+    * @param f
+    *   The function to apply to each vertex in the context of an accumulator.
+    * @return
+    *   The accumulated value.
+    */
   def dfsFold[Acc](
     graph: Graph,
     initial: Acc,
@@ -84,7 +94,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    graph.selectRoots().foreach { root =>
+    graph.view.foreach { root =>
+      if !discovered(root.ordinal) then
         val _ = s.push(root)
         while !s.isEmpty
         do
@@ -92,7 +103,8 @@ object GraphTraversal:
           if !discovered(v.ordinal) then
             acc = f(acc, v)
             discovered(v.ordinal) = true
-          graph.neighbors(v).foreach(w => s.push(w))
+            val _ = graph.neighbors(v).reverseIterator.foreach(s.push)
+          else ()
       else ()
     }
 
@@ -101,9 +113,6 @@ object GraphTraversal:
   /** Depth-first search that executes a side-effecting function on each
     * [[Vertex]], accepting the data stored for that [[Vertex]] as input.
     *
-    * This implementation performs DFS for _each root_ in the input
-    * [[AnyGraphWithData]].
-    *
     * @param graph
     *   The input [[Graph]] on which to run DFS.
     * @param visit
@@ -116,7 +125,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    graph.selectRoots().foreach { root =>
+    graph.view.foreach { root =>
+      if !discovered(root.ordinal) then
         val _ = s.push(root)
         while !s.isEmpty
         do
@@ -124,7 +134,8 @@ object GraphTraversal:
           if !discovered(v.ordinal) then
             val _ = visit(v, graph.data(v.ordinal))
             discovered(v.ordinal) = true
-          graph.neighbors(v).foreach(w => s.push(w))
+            val _ = graph.neighbors(v).reverseIterator.foreach(s.push)
+          else ()
       else ()
     }
 
@@ -133,9 +144,6 @@ object GraphTraversal:
   /** Depth-first search that executes a function on each [[Vertex]] to produce
     * some output, accepting the data stored for that [[Vertex]] as input.
     *
-    * This implementation performs DFS for _each root_ in the input
-    * [[AnyGraphWithData]].
-    *
     * @param graph
     *   The input [[Graph]] on which to run DFS.
     * @param visit
@@ -174,7 +182,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    graph.selectRoots().foreach { root =>
+    graph.view.foreach { root =>
+      if !discovered(root.ordinal) then
         val _ = s.push(root)
         while !s.isEmpty
         do
@@ -182,7 +191,8 @@ object GraphTraversal:
           if !discovered(v.ordinal) then
             acc = f(acc, graph.data(v.ordinal))
             discovered(v.ordinal) = true
-          graph.neighbors(v).foreach(w => s.push(w))
+            val _ = graph.neighbors(v).reverseIterator.foreach(s.push)
+          else ()
       else ()
     }
 
@@ -194,8 +204,10 @@ object GraphTraversal:
   ): Unit =
     val q       = Queue.empty[Vertex]
     val visited = Array.fill(graph.numberOfVertices.value)(false)
-    val _       = graph.selectRoots().foreach(q.enqueue)
 
+    graph.view.foreach { root =>
+      if !visited(root.ordinal) then
+        val _ = q.enqueue(root)
         while !q.isEmpty
         do
           val v = q.dequeue()
@@ -207,6 +219,8 @@ object GraphTraversal:
               else ()
             }
           else ()
+      else ()
+    }
 
   def bfs[Out](
     graph: Graph,
@@ -215,8 +229,10 @@ object GraphTraversal:
     val output  = ListBuffer.empty[Out]
     val q       = Queue.empty[Vertex]
     val visited = Array.fill(graph.numberOfVertices.value)(false)
-    val _       = graph.selectRoots().foreach(q.enqueue)
 
+    graph.view.foreach { root =>
+      if !visited(root.ordinal) then
+        val _ = q.enqueue(root)
         while !q.isEmpty
         do
           val v = q.dequeue()
@@ -228,6 +244,8 @@ object GraphTraversal:
               else ()
             }
           else ()
+      else ()
+    }
 
     output.toList
 
@@ -239,8 +257,10 @@ object GraphTraversal:
     var acc     = initial
     val q       = Queue.empty[Vertex]
     val visited = Array.fill(graph.numberOfVertices.value)(false)
-    val _       = graph.selectRoots().foreach(q.enqueue)
 
+    graph.view.foreach { root =>
+      if !visited(root.ordinal) then
+        val _ = q.enqueue(root)
         while !q.isEmpty
         do
           val v = q.dequeue()
@@ -252,6 +272,8 @@ object GraphTraversal:
               else ()
             }
           else ()
+      else ()
+    }
 
     acc
 

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

@@ -0,0 +1,200 @@
+package gs.graph.v0
+
+import gs.graph.v0.BfsTraversalTests.Counter
+import gs.graph.v0.BfsTraversalTests.Tracker
+import gs.graph.v0.directed.Digraph
+import munit.*
+import scala.collection.mutable.ListBuffer
+
+class BfsTraversalTests extends FunSuite:
+
+  test("should perform BFS on an empty graph") {
+    val c1 = new Counter
+    val _  = GraphTraversal.bfs(graph = UndirectedGraph.Empty, visit = c1.visit)
+    assertEquals(c1.count, 0)
+
+    val c2 = new Counter
+    val _  = GraphTraversal.bfs(graph = Digraph.Empty, visit = c2.visit)
+    assertEquals(c2.count, 0)
+  }
+
+  test("should perform BFS on a graph of size 1") {
+    val c1 = new Counter
+    val _ = GraphTraversal.bfs(graph = UndirectedGraph.Single, visit = c1.visit)
+    assertEquals(c1.count, 1)
+
+    val c2 = new Counter
+    val _  = GraphTraversal.bfs(graph = Digraph.Single, visit = c2.visit)
+    assertEquals(c2.count, 1)
+  }
+
+  test("should perform BFS on a complex directed graph") {
+    val n = Size(6)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = 0 -> 1,
+      1 -> 2,
+      2 -> 1,
+      0 -> 3,
+      3 -> 2,
+      4 -> 5
+    )
+    val expectedVisitOrder = List(0, 1, 3, 2, 4, 5)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.bfs(g, t.visit)
+    val o1                 = GraphTraversal.bfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.bfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform BFS on a DAG") {
+    val n = Size(4)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = 0 -> 1,
+      0 -> 2,
+      1 -> 3,
+      2 -> 3
+    )
+    val expectedVisitOrder = List(0, 1, 2, 3)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.bfs(g, t.visit)
+    val o1                 = GraphTraversal.bfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.bfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform BFS on a strongly connected graph") {
+    val n = Size(3)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = 0 -> 1,
+      1 -> 2,
+      2 -> 0
+    )
+    val expectedVisitOrder = List(0, 1, 2)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.bfs(g, t.visit)
+    val o1                 = GraphTraversal.bfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.bfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform BFS on a line") {
+    val n = Size(4)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = 0 -> 1,
+      1 -> 2,
+      2 -> 3
+    )
+    val expectedVisitOrder = List(0, 1, 2, 3)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.bfs(g, t.visit)
+    val o1                 = GraphTraversal.bfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.bfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform BFS on a larger complex digraph") {
+    val n = Size(10)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = 0 -> 1,
+      1 -> 2,
+      2 -> 3,
+      3 -> 6,
+      4 -> 5,
+      5 -> 6,
+      6 -> 7,
+      7 -> 8,
+      8 -> 9,
+      9 -> 6,
+      6 -> 8
+    )
+    val expectedVisitOrder = List(0, 1, 2, 3, 6, 7, 8, 9, 4, 5)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.bfs(g, t.visit)
+    val o1                 = GraphTraversal.bfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.bfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+object BfsTraversalTests:
+
+  trait BasicVisitor:
+    def visit(v: Vertex): Unit
+
+  class Counter extends BasicVisitor:
+
+    var count: Int = 0
+
+    def visit(v: Vertex): Unit =
+      count = count + 1
+      ()
+
+  end Counter
+
+  class Tracker extends BasicVisitor:
+
+    private val output: ListBuffer[Int] = ListBuffer.empty
+
+    def snapshot(): List[Int] = output.toList
+
+    def visit(v: Vertex): Unit =
+      val _ = output.addOne(v.ordinal)
+      ()
+
+  end Tracker
+
+end BfsTraversalTests

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

@@ -0,0 +1,203 @@
+package gs.graph.v0
+
+import gs.graph.v0.DfsTraversalTests.Counter
+import gs.graph.v0.DfsTraversalTests.Tracker
+import gs.graph.v0.directed.Digraph
+import munit.*
+import scala.collection.mutable.ListBuffer
+
+class DfsTraversalTests extends FunSuite:
+
+  test("should perform DFS on an empty graph") {
+    val c1 = new Counter
+    val _  = GraphTraversal.dfs(graph = UndirectedGraph.Empty, visit = c1.visit)
+    assertEquals(c1.count, 0)
+
+    val c2 = new Counter
+    val _  = GraphTraversal.dfs(graph = Digraph.Empty, visit = c2.visit)
+    assertEquals(c2.count, 0)
+  }
+
+  test("should perform DFS on a graph of size 1") {
+    val c1 = new Counter
+    val _ = GraphTraversal.dfs(graph = UndirectedGraph.Single, visit = c1.visit)
+    assertEquals(c1.count, 1)
+
+    val c2 = new Counter
+    val _  = GraphTraversal.dfs(graph = Digraph.Single, visit = c2.visit)
+    assertEquals(c2.count, 1)
+  }
+
+  test("should perform DFS on a complex directed graph") {
+    // This test case includes:
+    // - Cycles
+    // - Multi-Root (0 and 4 are the roots)
+    val n = Size(6)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = (0, 1),
+      (1, 2),
+      (2, 1),
+      (0, 3),
+      (3, 2),
+      (4, 5)
+    )
+    val expectedVisitOrder = List(0, 1, 2, 3, 4, 5)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.dfs(g, t.visit)
+    val o1                 = GraphTraversal.dfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.dfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform DFS on a DAG") {
+    val n = Size(4)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = (0, 1),
+      (0, 2),
+      (1, 3),
+      (2, 3)
+    )
+    val expectedVisitOrder = List(0, 1, 3, 2)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.dfs(g, t.visit)
+    val o1                 = GraphTraversal.dfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.dfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform DFS on a strongly connected graph") {
+    val n = Size(3)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = (0, 1),
+      (1, 2),
+      (2, 0)
+    )
+    val expectedVisitOrder = List(0, 1, 2)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.dfs(g, t.visit)
+    val o1                 = GraphTraversal.dfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.dfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform DFS on a line") {
+    val n = Size(4)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = (0, 1),
+      (1, 2),
+      (2, 3)
+    )
+    val expectedVisitOrder = List(0, 1, 2, 3)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.dfs(g, t.visit)
+    val o1                 = GraphTraversal.dfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.dfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+  test("should perform DFS on a larger complex digraph") {
+    val n = Size(10)
+    val g = Graph.directed(
+      numberOfVertices = n,
+      edges = 0 -> 1,
+      1 -> 2,
+      2 -> 3,
+      3 -> 6,
+      4 -> 5,
+      5 -> 6,
+      6 -> 7,
+      7 -> 8,
+      8 -> 9,
+      9 -> 6,
+      6 -> 8
+    )
+    val expectedVisitOrder = List(0, 1, 2, 3, 6, 7, 8, 9, 4, 5)
+    val t                  = new Tracker
+    val b                  = ListBuffer.empty[Int]
+    val _                  = GraphTraversal.dfs(g, t.visit)
+    val o1                 = GraphTraversal.dfs(g, v => v.ordinal)
+    val o2                 = GraphTraversal.dfsFold(
+      g,
+      b,
+      (
+        acc,
+        vx
+      ) => acc.addOne(vx.ordinal)
+    )
+    assertEquals(t.snapshot(), expectedVisitOrder)
+    assertEquals(o1, expectedVisitOrder)
+    assertEquals(o2.toList, expectedVisitOrder)
+  }
+
+object DfsTraversalTests:
+
+  trait BasicVisitor:
+    def visit(v: Vertex): Unit
+
+  class Counter extends BasicVisitor:
+
+    var count: Int = 0
+
+    def visit(v: Vertex): Unit =
+      count = count + 1
+      ()
+
+  end Counter
+
+  class Tracker extends BasicVisitor:
+
+    private val output: ListBuffer[Int] = ListBuffer.empty
+
+    def snapshot(): List[Int] = output.toList
+
+    def visit(v: Vertex): Unit =
+      val _ = output.addOne(v.ordinal)
+      ()
+
+  end Tracker
+
+end DfsTraversalTests

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

@@ -0,0 +1,28 @@
+package gs.graph.v0
+
+import munit.*
+
+class GraphDispositionTests extends FunSuite:
+
+  test("should parse and match all defined dispositions") {
+    val d1 = GraphDisposition.Directed
+    val d2 = GraphDisposition.Undirected
+    assertEquals(d1, GraphDisposition.Directed)
+    assertEquals(d2, GraphDisposition.Undirected)
+    assertEquals(d1.equals(d2), false)
+    assertEquals(d1.hashCode(), GraphDisposition.Directed.hashCode())
+    assertEquals(d2.hashCode(), GraphDisposition.Undirected.hashCode())
+    assertEquals(d1.toString(), GraphDisposition.Directed.name)
+    assertEquals(d2.toString(), GraphDisposition.Undirected.name)
+    assertEquals(d1.equals(null), false)
+    assertEquals(d1.equals("foo"), false)
+    assertEquals(d1.equals(1), false)
+
+    val p1 = GraphDisposition.parse(d1.name)
+    val p2 = GraphDisposition.parse(d2.name)
+    val p3 = GraphDisposition.parse("something else")
+
+    assertEquals(p3, None)
+    assertEquals(p1, Some(d1))
+    assertEquals(p2, Some(d2))
+  }

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

@@ -17,19 +17,38 @@ class VertexTests extends FunSuite:
     assertEquals(v1.hashCode(), v2.hashCode())
     assertNotEquals(v1.hashCode(), v3.hashCode())
     assertEquals(v1 < v3, true)
+    assertEquals(v1 <= v3, true)
     assertEquals(v1 < v2, false)
+    assertEquals(v1 <= v2, true)
     assertEquals(v1 > v3, false)
+    assertEquals(v1 >= v3, false)
     assertEquals(v3 > v1, true)
+    assertEquals(v3 >= v1, true)
+    assertEquals(v2 >= v1, true)
+    assertEquals(v2 > v1, false)
     assertEquals(v1 < 3, true)
+    assertEquals(v1 <= 3, true)
     assertEquals(v1 < 0, false)
+    assertEquals(v1 <= 0, true)
     assertEquals(v1 > 0, false)
+    assertEquals(v1 >= 0, true)
     assertEquals(v3 > 0, true)
+    assertEquals(v3 >= 0, true)
     assertEquals(v1 < Size(3), true)
+    assertEquals(v1 <= Size(3), true)
     assertEquals(v1 < Size.Zero, false)
+    assertEquals(v1 <= Size.Zero, true)
     assertEquals(v1 > Size.Zero, false)
+    assertEquals(v1 >= Size.Zero, true)
     assertEquals(v3 > Size.Zero, true)
+    assertEquals(v3 >= Size.Zero, true)
     assertEquals(v1.toString(), v2.toString())
     assertNotEquals(v1.toString(), v3.toString())
+    assertEquals(v1.compare(v3), -3)
+    assertEquals(v1.compare(v2), 0)
+    assertEquals(v1.value, 0)
+    assertEquals(v2.value, 0)
+    assertEquals(v3.value, 3)
   }
 
   test("should throw an exception if an invalid value is given") {
@@ -38,3 +57,26 @@ class VertexTests extends FunSuite:
       case Some(cause) =>
         assertEquals(cause.getMessage(), "Vertex values must be 0 or greater.")
   }
+
+  test("should instantiate a list of vertices") {
+    val vs = Vertex.list(0, 1, 2, 3)
+    assertEquals(vs, List(0, 1, 2, 3).map(Vertex(_)))
+  }
+
+  test("should instantiate a set of vertices") {
+    val vs = Vertex.set(0, 1, 2, 3, 0, 1, 2, 3)
+    assertEquals(vs, Set(0, 1, 2, 3).map(Vertex(_)))
+  }
+
+  test("should support the ordering type class") {
+    val o  = Ordering[Vertex]
+    val v1 = Vertex(0)
+    val v2 = Vertex(0)
+    val v3 = Vertex(1)
+    val v4 = Vertex(2)
+    assertEquals(o.compare(v1, v2), 0)
+    assertEquals(o.compare(v1, v3), -1)
+    assertEquals(o.compare(v1, v4), -2)
+    assertEquals(o.compare(v4, v1), 2)
+    assertEquals(o.compare(v4, v3), 1)
+  }