A null graph is not a valid tree

Author: clue

lib/Fhaculty/Graph/Algorithm/Tree/Base.php

@@ -10,6 +10,7 @@
 use Fhaculty\Graph\Exception\UnexpectedValueException;
 use Fhaculty\Graph\Algorithm\Search\StrictDepthFirst;
 use Fhaculty\Graph\Algorithm\Degree;
+use Fhaculty\Graph\Algorithm\ConnectedComponents;
 
 /**
  * Abstract base class for tree algorithms
@@ -18,7 +19,9 @@
  * graphs that represent a tree.
  *
  * A tree is a connected Graph (single component) with no cycles. Every Tree is
- * a Graph, but not every Graph is a Tree.
+ * a Graph, but not every Graph is a Tree. A null Graph (a Graph with no Vertices
+ * and thus no Edges) is *NOT* considered a valid Tree, as it is not considered
+ * connected (@see ConnectedComponents and @link)
  *
  *    A
  *   / \
@@ -32,6 +35,7 @@
  *
  * @link http://en.wikipedia.org/wiki/Tree_%28graph_theory%29
  * @link http://en.wikipedia.org/wiki/Tree_%28data_structure%29
+ * @link http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree
  * @see Undirected for an implementation of these algorithms on (undirected) trees
  * @see BaseDirected for an abstract implementation of these algorithms on directed, rooted trees
  */

lib/Fhaculty/Graph/Algorithm/Tree/BaseDirected.php

@@ -73,16 +73,11 @@ public function getVertexRoot()
      * checks if this is a tree
      *
      * @return boolean
-     * @uses Vertices::isEmpty() to skip empty Graphs (an empty Graph is a valid tree)
      * @uses self::getVertexRoot() to get root Vertex to start search from
      * @uses self::getVerticesSubtree() to count number of vertices connected to root
      */
     public function isTree()
     {
-        if ($this->graph->getVertices()->isEmpty()) {
-            return true;
-        }
-
         try {
             $root = $this->getVertexRoot();
         }
@@ -138,7 +133,7 @@ abstract public function getVerticesChildren(Vertex $vertex);
     /**
      * internal helper to get all parents vertices
      *
-     * a valid tree vertex only ever has a single parent, expect for the root,
+     * a valid tree vertex only ever has a single parent, except for the root,
      * which has none.
      *
      * @param Vertex $vertex

lib/Fhaculty/Graph/Algorithm/Tree/Undirected.php

@@ -49,14 +49,14 @@ class Undirected extends Tree
      * checks if this is a tree
      *
      * @return boolean
-     * @uses Vertices::isEmpty() to skip empty Graphs (an empty Graph is a valid tree)
+     * @uses Vertices::isEmpty() to skip null Graphs (a Graph with no Vertices is *NOT* a valid tree)
      * @uses Graph::getVertexFirst() to get get get random "root" Vertex to start search from
      * @uses self::getVerticesSubtreeRecursive() to count number of vertices connected to root
      */
     public function isTree()
     {
         if ($this->graph->getVertices()->isEmpty()) {
-            return true;
+            return false;
         }
 
         // every vertex can represent a root vertex, so just pick one

tests/Fhaculty/Graph/Algorithm/Tree/BaseDirectedTest.php

@@ -30,12 +30,12 @@ abstract protected function createGraphTree();
      */
     abstract protected function createGraphParallelEdge();
 
-    public function testEmptyGraph()
+    public function testNullGraph()
     {
         $graph = new Graph();
 
         $tree = $this->createTreeAlg($graph);
-        $this->assertTrue($tree->isTree());
+        $this->assertFalse($tree->isTree());
         $this->assertTrue($tree->getVerticesLeaf()->isEmpty());
         $this->assertTrue($tree->getVerticesInternal()->isEmpty());
 
@@ -44,7 +44,7 @@ public function testEmptyGraph()
 
     /**
      * @param BaseDirected $tree
-     * @depends testEmptyGraph
+     * @depends testNullGraph
      * @expectedException UnderflowException
      */
     public function testEmptyGraphDoesNotHaveRootVertex(BaseDirected $tree)
@@ -54,7 +54,7 @@ public function testEmptyGraphDoesNotHaveRootVertex(BaseDirected $tree)
 
     /**
      * @param BaseDirected $tree
-     * @depends testEmptyGraph
+     * @depends testNullGraph
      * @expectedException UnderflowException
      */
     public function testEmptyGraphDoesNotHaveDegree(BaseDirected $tree)
@@ -64,7 +64,7 @@ public function testEmptyGraphDoesNotHaveDegree(BaseDirected $tree)
 
     /**
      * @param BaseDirected $tree
-     * @depends testEmptyGraph
+     * @depends testNullGraph
      * @expectedException UnderflowException
      */
     public function testEmptyGraphDoesNotHaveHeight(BaseDirected $tree)

tests/Fhaculty/Graph/Algorithm/Tree/UndirectedTest.php

@@ -11,15 +11,15 @@ protected function createTree(Graph $graph)
         return new Undirected($graph);
     }
 
-    public function testGraphEmpty()
+    public function testNullGraph()
     {
         $graph = new Graph();
 
         $tree = $this->createTree($graph);
 
-        $this->assertTrue($tree->isTree());
-        $this->assertSame(array(), $tree->getVerticesInternal()->getVector());
-        $this->assertSame(array(), $tree->getVerticesLeaf()->getVector());
+        $this->assertFalse($tree->isTree());
+        $this->assertTrue($tree->getVerticesInternal()->isEmpty());
+        $this->assertTrue($tree->getVerticesLeaf()->isEmpty());
     }
 
     public function testGraphTrivial()