diff --git a/TinySTL/Detail/Graph.impl.h b/TinySTL/Detail/Graph.impl.h
index d8ec21d..25e6edb 100644
--- a/TinySTL/Detail/Graph.impl.h
+++ b/TinySTL/Detail/Graph.impl.h
@@ -106,6 +106,23 @@ namespace TinySTL{
 					DFS(n.first, func);
 			}
 		}
+		template<class Index, class Value, class EqualFunc>
+		string graph<Index, Value, EqualFunc>::to_string(){
+			string str;
+			std::ostringstream oss;
+			for (auto oit = begin(); oit != end(); ++oit){
+				
+				oss << "[" << oit->first << "," << oit->second << "]" << ":";
+				auto eit = end(oit->first);
+				for (auto iit = begin(oit->first); iit != eit; ++iit){
+					oss << "[" << iit->first << ", " << iit->second << "]" << "-";
+				}
+				oss << "[NULL,NULL]" << std::endl << std::setw(4) << "|" << std::endl;
+			}
+			oss << "[NULL,NULL]" << std::endl;
+			str.append(oss.str().c_str());
+			return str;
+		}
 		//********************************************************************************
 		template<class Index, class Value, class EqualFunc>
 		inner_iterator<Index, Value, EqualFunc>& inner_iterator<Index, Value, EqualFunc>::operator ++(){
@@ -155,17 +172,13 @@ namespace TinySTL{
 	template<class Index, class Value, class EqualFunc>
 	directed_graph<Index, Value, EqualFunc>::directed_graph():graph(){}
 	template<class Index, class Value, class EqualFunc>
-	void directed_graph<Index, Value, EqualFunc>::add_node(const node& n, const node_sets& nodes){
-		if (!is_contained(n.first)){
-			nodes_.push_front(make_pair(n, list<typename graph::node>()));
-			++size_;
-		}
+	void directed_graph<Index, Value, EqualFunc>::add_node_helper(const Index& index, const node_sets& nodes){
 		if (nodes.empty())
 			return;
 		//find node n's list
 		list<typename graph::node>* l;
 		for (auto& pair : nodes_){
-			if (equal_func(pair.first.first, n.first))
+			if (equal_func(pair.first.first, index))
 				l = &(pair.second);
 		}
 		for (const auto& item : nodes){
@@ -175,4 +188,16 @@ namespace TinySTL{
 			}
 		}
 	}
+	template<class Index, class Value, class EqualFunc>
+	void directed_graph<Index, Value, EqualFunc>::add_node(const node& n, const node_sets& nodes){
+		if (!is_contained(n.first)){
+			nodes_.push_front(make_pair(n, list<typename graph::node>()));
+			++size_;
+		}
+		add_node_helper(n.first, nodes);
+	}
+	template<class Index, class Value, class EqualFunc>
+	void directed_graph<Index, Value, EqualFunc>::add_node(const Index& index, const node_sets& nodes){
+		add_node_helper(index, nodes);
+	}
 }
\ No newline at end of file
diff --git a/TinySTL/Graph.h b/TinySTL/Graph.h
index 656d5f5..363abcd 100644
--- a/TinySTL/Graph.h
+++ b/TinySTL/Graph.h
@@ -3,11 +3,14 @@
 
 #include "Allocator.h"
 #include "List.h"
+#include "String.h"
 #include "Unordered_set.h"
 #include "Utility.h"
 #include "Vector.h"
 
 #include <functional>
+#include <iomanip>
+#include <sstream>
 
 namespace TinySTL{
 	namespace Detail{
@@ -17,7 +20,7 @@ namespace TinySTL{
 		class outter_iterator;
 
 		template<class Index, class Value, class EqualFunc = equal_to<Index>>
-		class graph{
+		class graph{//base class
 		public:
 			friend class inner_iterator < Index, Value, EqualFunc >;
 			friend class outter_iterator < Index, Value, EqualFunc > ;
@@ -35,7 +38,10 @@ namespace TinySTL{
 			graph() :size_(0){};
 			virtual ~graph(){ cleanup(); };
 
+			//node can be not in the graph
 			virtual void add_node(const node& item, const node_sets& nodes) = 0;
+			//node of the index must in the graph
+			virtual void add_node(const Index& index, const node_sets& nodes) = 0;
 			//virtual void delte_node(const node& item) = 0;
 
 			void DFS(const Index& index, visiter_func_type func);
@@ -56,6 +62,8 @@ namespace TinySTL{
 			inline inner_iterator end(const Index& index);
 			inline iterator begin();
 			inline iterator end();
+
+			string to_string();
 		protected:
 			list<pair<node, list<node>>> nodes_;
 			equal_func_type equal_func;
@@ -124,6 +132,9 @@ namespace TinySTL{
 		~directed_graph(){}
 		//node n -> every node in the nodes set
 		void add_node(const node& n, const node_sets& nodes) override;
+		void add_node(const Index& index, const node_sets& nodes) override;
+	private:
+		void add_node_helper(const Index& index, const node_sets& nodes);
 	};
 }