diff --git a/Stdlib/Graph/BinaryTree.php b/Stdlib/Graph/BinaryTree.php
index 4f481ea45..bad8940e0 100644
--- a/Stdlib/Graph/BinaryTree.php
+++ b/Stdlib/Graph/BinaryTree.php
@@ -46,11 +46,11 @@ class BinaryTree extends Tree
 	}
 
 	public function getLeft() {
-		return $this->nodes[0];
+		return $this->nodes[0] ?? null;
 	}
 
 	public function getRight() {
-		return $this->nodes[1];
+		return $this->nodes[1] ?? null;
 	}
 
 	public function setLeft(BinaryTree $left) {
@@ -61,7 +61,80 @@ class BinaryTree extends Tree
 		$this->nodes[1] = $right;
 	}
 
-	public function inOrder() {
-		
+	public function preOrder(\Closure $callback) {
+		if(count($this->nodes) === 0) {
+			return;
+		}
+
+		$callback($this);
+		$this->nodes[0]->inOrder($callback);
+		$this->nodes[1]->inOrder($callback);
+	}
+
+	public function inOrder(\Closure $callback) {
+		if(count($this->nodes) === 0) {
+			return;
+		}
+
+		$this->nodes[0]->inOrder($callback);
+		$callback($this);
+		$this->nodes[1]->inOrder($callback);
+	}
+
+	public function postOrder(\Closure $callback) {
+		if(count($this->nodes) === 0) {
+			return;
+		}
+
+		$this->nodes[0]->inOrder($callback);
+		$this->nodes[1]->inOrder($callback);
+		$callback($this);
+	}
+
+	private function getVerticalOrder(int $horizontalDistance = 0, array &$order) 
+	{
+		if(!isset($order[$horizontalDistance])) {
+			$order[$horizontalDistance] = [];
+		}
+
+		$order[$horizontalDistance][] = $this;
+
+		if(isset($this->nodes[0])) {
+			$this->nodes[0]->getVerticalOrder($horizontalDistance-1, $order);
+		}
+
+		if(isset($this->nodes[1])) {
+			$this->nodes[1]->getVerticalOrder($horizontalDistance+1, $order);
+		}
+	}
+
+	public function verticalOrder(\Closure $callback)
+	{
+		$order = [];
+		$this->getVerticalOrder(0, $order);
+
+		foreach($order as $level) {
+			foreach($level as $node) {
+				$callback($node);
+			}
+		}
+	}
+
+	public function isSymmetric() : bool {
+		// todo: compare values? true symmetry requires the values to be the same
+		if(isset($this->nodes[0]) && isset($this->nodes[1])) {
+			return isSymmetric($this->nodes[0], $this->nodes[1]);
+		}
+
+		return false;
+	}
+
+	public function symmetric(BinaryTree $tree1, BinaryTree $tree2) : bool {
+		// todo: compare values? true symmetry requires the values to be the same
+		if(($tree1 !== null && $tree2 !== null) || $tree1 === $tree2) {
+			return isSymmetric($tree1->getLeft(), $tree1->getRight()) && isSymmetric($tree2->getRight(), $tree2->getLeft());
+		}
+
+		return false;
 	}
 }
\ No newline at end of file
diff --git a/Stdlib/Graph/Tree.php b/Stdlib/Graph/Tree.php
index 4d1a29e36..82514b0cc 100644
--- a/Stdlib/Graph/Tree.php
+++ b/Stdlib/Graph/Tree.php
@@ -32,6 +32,18 @@ class Tree extends Graph
 {
 	protected $nodes = [];
 
+	public function add(Tree $node) {
+		$this->nodes[] = $node;
+
+		return $this;
+	}
+
+	public function set($key, Tree $node) {
+		$this->nodes[$key] = $node;
+
+		return $this;
+	}
+
 	public function getMaxDepth() : int 
 	{
 		$depth = [0];
@@ -54,42 +66,44 @@ class Tree extends Graph
 		return min($depth) + 1;
 	}
 
-	public function postOrder() 
-	{
-
-	}
-
-	public function preOrder()
-	{
-
-	}
-
-	public function levelOrder()
-	{
-
-	}
-
-	public function levelOrder2()
-	{
-
-	}
-
-	public function verticalOrder()
+	public function levelOrder(\Closure $callback)
 	{
+		$depth = $this->getMaxDepth();
 
+		for($i = 1; $i < $depth; $i++) {
+			$nodes = $this->getLevel($i);
+			callback($nodes);
+		}
 	}
 
 	public function isLeaf() : bool 
 	{
-
-	}
-
-	public function isSymmetric() : bool {
-
+		return count($this->nodes) === 0;
 	}
 
 	public function getDimension() : int 
 	{
-		
+		$size = 1;
+
+		foreach($this->nodes as $node) {
+			$size += $node->getDimension() + 1;
+		}
+
+		return $size;
+	}
+
+	public function getLevelNodes(int $level, array &$nodes)
+	{
+		--$level;
+
+		foreach($this->nodes as $node) {
+			if($level === 0) {
+				$nodes[] = $this;
+
+				return $nodes;
+			} else {
+				$this->getLevelNodes($level, $nodes);
+			}
+		}
 	}
 }
\ No newline at end of file