diff --git a/paddle/fluid/framework/details/multi_devices_graph_builder.cc b/paddle/fluid/framework/details/multi_devices_graph_builder.cc
index 4cc6e5727b2bc1b3e1bba03b0a1de40125f1ef54..4050424e7012ae6463d4fea1f99aa94de0fa838b 100644
--- a/paddle/fluid/framework/details/multi_devices_graph_builder.cc
+++ b/paddle/fluid/framework/details/multi_devices_graph_builder.cc
@@ -68,7 +68,8 @@ MultiDevSSAGraphBuilder::MultiDevSSAGraphBuilder(
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateOpHandleIOs(Graph *result, ir::Node *node,
+void MultiDevSSAGraphBuilder::CreateOpHandleIOs(ir::Graph *result,
+                                                ir::Node *node,
                                                 size_t place_id) const {
   auto p = places_[place_id];
   auto *op_handle = result->Get<GraphOps>("ops").back().get();
@@ -192,8 +193,9 @@ size_t MultiDevSSAGraphBuilder::GetAppropriateDeviceID(
 // to parameter/gradients before optimizer ops, topo sort is insufficient. (
 // some optimizer ops might not depend on any nodes), we manually move all
 // optimizer nodes after last backward nodes.
-std::vector<ir::Node *> SortOpsAndDelayOptimizeOp(const Graph &graph) {
-  std::vector<ir::Node *> ret = ir::TopologySort(graph);
+// However, the assumption by SSAGraphBuilder should be relaxed in the future.
+std::vector<ir::Node *> SortOpsAndDelayOptimizeOp(const ir::Graph &graph) {
+  std::vector<ir::Node *> ret = ir::TopologySortOperations(graph);
   size_t last_backward = 0;
   std::vector<ir::Node *> optimize_ops;
   std::vector<ir::Node *> sorted_ret;
@@ -232,8 +234,8 @@ std::vector<ir::Node *> SortOpsAndDelayOptimizeOp(const Graph &graph) {
   return sorted_ret;
 }
 
-std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
-    std::unique_ptr<Graph> graph) const {
+std::unique_ptr<ir::Graph> MultiDevSSAGraphBuilder::Apply(
+    std::unique_ptr<ir::Graph> graph) const {
   // Rebuild the graph structure.
   std::vector<ir::Node *> sorted_ops = SortOpsAndDelayOptimizeOp(*graph);
   auto nodes = std::move(graph->nodes);
@@ -245,7 +247,7 @@ std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
     }
   }
 
-  Graph &result = *graph;
+  ir::Graph &result = *graph;
   std::unordered_set<std::string> og_has_been_broadcast;
 
   // We cannot invoke resize. It is a bug of GCC 4.8
@@ -397,7 +399,7 @@ void MultiDevSSAGraphBuilder::SetCommunicationContext(
 #endif
 }
 
-void MultiDevSSAGraphBuilder::CreateBroadcastOp(Graph *result,
+void MultiDevSSAGraphBuilder::CreateBroadcastOp(ir::Graph *result,
                                                 const std::string &p_name,
                                                 size_t src_dev_id) const {
 #ifdef PADDLE_WITH_CUDA
@@ -427,7 +429,7 @@ void MultiDevSSAGraphBuilder::CreateBroadcastOp(Graph *result,
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateComputationalOp(Graph *result,
+void MultiDevSSAGraphBuilder::CreateComputationalOp(ir::Graph *result,
                                                     ir::Node *node,
                                                     int dev_id) const {
   result->Get<GraphOps>("ops").emplace_back(
@@ -436,7 +438,7 @@ void MultiDevSSAGraphBuilder::CreateComputationalOp(Graph *result,
   CreateOpHandleIOs(result, node, dev_id);
 }
 
-void MultiDevSSAGraphBuilder::InsertAllReduceOp(Graph *result,
+void MultiDevSSAGraphBuilder::InsertAllReduceOp(ir::Graph *result,
                                                 const std::string &og) const {
 #ifdef PADDLE_WITH_CUDA
   result->Get<GraphOps>("ops").emplace_back(new AllReduceOpHandle(
@@ -466,7 +468,7 @@ void MultiDevSSAGraphBuilder::InsertAllReduceOp(Graph *result,
 }
 
 void MultiDevSSAGraphBuilder::InsertDataBalanceOp(
-    Graph *result, const std::vector<std::string> &datas) const {
+    ir::Graph *result, const std::vector<std::string> &datas) const {
 #ifdef PADDLE_WITH_CUDA
   result->Get<GraphOps>("ops").emplace_back(new DataBalanceOpHandle(
       result->CreateEmptyNode("data_balance", ir::Node::Type::kOperation),
@@ -529,7 +531,7 @@ int MultiDevSSAGraphBuilder::GetVarDeviceID(const std::string &varname) const {
   return got == var_name_on_devices_.end() ? -1 : got->second;
 }
 
-void MultiDevSSAGraphBuilder::CreateScaleLossGradOp(Graph *result) const {
+void MultiDevSSAGraphBuilder::CreateScaleLossGradOp(ir::Graph *result) const {
   for (size_t i = 0; i < places_.size(); ++i) {
 // Insert ScaleCost OpHandle
 #ifdef PADDLE_WITH_CUDA
@@ -559,7 +561,7 @@ void MultiDevSSAGraphBuilder::CreateScaleLossGradOp(Graph *result) const {
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateComputationalOps(Graph *result,
+void MultiDevSSAGraphBuilder::CreateComputationalOps(ir::Graph *result,
                                                      ir::Node *node,
                                                      size_t num_places) const {
   for (size_t scope_idx = 0; scope_idx < num_places; ++scope_idx) {
@@ -571,7 +573,7 @@ void MultiDevSSAGraphBuilder::CreateComputationalOps(Graph *result,
   }
 }
 
-VarHandle *MultiDevSSAGraphBuilder::CreateReduceOp(Graph *result,
+VarHandle *MultiDevSSAGraphBuilder::CreateReduceOp(ir::Graph *result,
                                                    const std::string &og,
                                                    int dst_dev_id) const {
 #ifdef PADDLE_WITH_CUDA
@@ -604,7 +606,7 @@ VarHandle *MultiDevSSAGraphBuilder::CreateReduceOp(Graph *result,
 
 // Find the first occurence of `prev_op_name` and make current `op` depend
 // on it.
-void MultiDevSSAGraphBuilder::ConnectOp(Graph *result, OpHandleBase *op,
+void MultiDevSSAGraphBuilder::ConnectOp(ir::Graph *result, OpHandleBase *op,
                                         const std::string &prev_op_name) const {
   for (auto &prev_op : result->Get<GraphOps>("ops")) {
     if (prev_op->Name() == prev_op_name) {
@@ -617,7 +619,7 @@ void MultiDevSSAGraphBuilder::ConnectOp(Graph *result, OpHandleBase *op,
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateDistTrainOp(Graph *result,
+void MultiDevSSAGraphBuilder::CreateDistTrainOp(ir::Graph *result,
                                                 ir::Node *node) const {
   int op_dev_id = -1;
   std::vector<std::string> input_var_names;
@@ -664,7 +666,8 @@ void MultiDevSSAGraphBuilder::CreateDistTrainOp(Graph *result,
 }
 
 // Create RPC related op handles that connects its in ops and out ops.
-void MultiDevSSAGraphBuilder::CreateRPCOp(Graph *result, ir::Node *node) const {
+void MultiDevSSAGraphBuilder::CreateRPCOp(ir::Graph *result,
+                                          ir::Node *node) const {
   int op_dev_id = -1;
   if (node->Op()->Type() == "send") {
     op_dev_id = GetVarDeviceID(node->inputs[0]->Name());
diff --git a/paddle/fluid/framework/details/multi_devices_graph_builder.h b/paddle/fluid/framework/details/multi_devices_graph_builder.h
index 2b7f4f586b4e750fde9245286c977258a9db6086..c2c764bb9443ab932f4460341c3abfd403e7b5eb 100644
--- a/paddle/fluid/framework/details/multi_devices_graph_builder.h
+++ b/paddle/fluid/framework/details/multi_devices_graph_builder.h
@@ -46,11 +46,13 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
                           const std::vector<Scope *> &local_scopes,
                           const BuildStrategy &strategy);
 #endif
-  std::unique_ptr<Graph> Apply(std::unique_ptr<Graph> graph) const override;
+  std::unique_ptr<ir::Graph> Apply(
+      std::unique_ptr<ir::Graph> graph) const override;
   int GetVarDeviceID(const std::string &varname) const override;
 
  private:
-  void CreateOpHandleIOs(Graph *result, ir::Node *node, size_t device_id) const;
+  void CreateOpHandleIOs(ir::Graph *result, ir::Node *node,
+                         size_t device_id) const;
 
  private:
   std::string loss_var_name_;
@@ -64,8 +66,8 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
 
   bool IsScaleLossOp(ir::Node *node) const;
 
-  void CreateRPCOp(Graph *result, ir::Node *node) const;
-  void CreateDistTrainOp(Graph *result, ir::Node *node) const;
+  void CreateRPCOp(ir::Graph *result, ir::Node *node) const;
+  void CreateDistTrainOp(ir::Graph *result, ir::Node *node) const;
 
   /**
    * Is this operator as the end-point operator before/after send operator.
@@ -79,16 +81,17 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
   std::vector<std::string> FindDistTrainRecvVars(
       const std::vector<std::unique_ptr<ir::Node>> &nodes) const;
 
-  void ConnectOp(Graph *result, OpHandleBase *op,
+  void ConnectOp(ir::Graph *result, OpHandleBase *op,
                  const std::string &prev_op_name) const;
 
-  void CreateComputationalOps(Graph *result, ir::Node *node,
+  void CreateComputationalOps(ir::Graph *result, ir::Node *node,
                               size_t num_places) const;
 
-  void CreateScaleLossGradOp(Graph *result) const;
-  VarHandle *CreateReduceOp(Graph *result, const std::string &og,
+  void CreateScaleLossGradOp(ir::Graph *result) const;
+  VarHandle *CreateReduceOp(ir::Graph *result, const std::string &og,
                             int dst_dev_id) const;
-  void CreateComputationalOp(Graph *result, ir::Node *node, int dev_id) const;
+  void CreateComputationalOp(ir::Graph *result, ir::Node *node,
+                             int dev_id) const;
 
   bool IsParameterGradientOnce(
       const std::string &og,
@@ -96,12 +99,12 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
 
   int GetOpDeviceID(ir::Node *node) const;
 
-  void InsertAllReduceOp(Graph *result, const std::string &og) const;
+  void InsertAllReduceOp(ir::Graph *result, const std::string &og) const;
 
-  void InsertDataBalanceOp(Graph *result,
+  void InsertDataBalanceOp(ir::Graph *result,
                            const std::vector<std::string> &datas) const;
 
-  void CreateBroadcastOp(Graph *result, const std::string &p_name,
+  void CreateBroadcastOp(ir::Graph *result, const std::string &p_name,
                          size_t src_dev_id) const;
 
   bool IsSparseGradient(const std::string &og) const;
diff --git a/paddle/fluid/framework/details/ssa_graph_builder.cc b/paddle/fluid/framework/details/ssa_graph_builder.cc
index 2be4bb009eff2866f39f08f11052822eb1fdea5a..3c579f427e5a04ce3c144e3709451247b29c6fcc 100644
--- a/paddle/fluid/framework/details/ssa_graph_builder.cc
+++ b/paddle/fluid/framework/details/ssa_graph_builder.cc
@@ -17,7 +17,7 @@
 namespace paddle {
 namespace framework {
 namespace details {
-void SSAGraphBuilder::PolishGraphToSupportDataHazards(Graph *graph) {
+void SSAGraphBuilder::PolishGraphToSupportDataHazards(ir::Graph *graph) {
   for (auto &var_map : graph->Get<GraphVars>("vars")) {
     for (auto &name_pair : var_map) {
       if (name_pair.second.size() <= 1) {
@@ -60,7 +60,7 @@ void SSAGraphBuilder::PolishGraphToSupportDataHazards(Graph *graph) {
 }
 
 VarHandle *SSAGraphBuilder::CreateOrGetLatestVarHandle(
-    Graph *graph, ir::Node *node, const platform::Place &place,
+    ir::Graph *graph, ir::Node *node, const platform::Place &place,
     size_t place_offset) {
   auto &var_holders = graph->Get<GraphVars>("vars")[place_offset];
   auto &var_holder = var_holders[node->Name()];
@@ -81,7 +81,7 @@ VarHandle *SSAGraphBuilder::CreateOrGetLatestVarHandle(
   return var;
 }
 
-void SSAGraphBuilder::CreateOpOutput(Graph *graph, OpHandleBase *op_handle,
+void SSAGraphBuilder::CreateOpOutput(ir::Graph *graph, OpHandleBase *op_handle,
                                      ir::Node *new_node,
                                      const platform::Place &place,
                                      size_t place_offset) {
@@ -93,7 +93,7 @@ void SSAGraphBuilder::CreateOpOutput(Graph *graph, OpHandleBase *op_handle,
   op_handle->AddOutput(var);
 }
 
-void SSAGraphBuilder::AddOutputToLeafOps(Graph *graph) {
+void SSAGraphBuilder::AddOutputToLeafOps(ir::Graph *graph) {
   for (auto &op : graph->Get<GraphOps>("ops")) {
     if (!op->Outputs().empty()) {
       continue;
diff --git a/paddle/fluid/framework/details/ssa_graph_builder.h b/paddle/fluid/framework/details/ssa_graph_builder.h
index e8e8acdb38f893302fb92c47d6f1cb2d38453e0f..f64445b470a76766f5a8e6e106418a14f352ef11 100644
--- a/paddle/fluid/framework/details/ssa_graph_builder.h
+++ b/paddle/fluid/framework/details/ssa_graph_builder.h
@@ -64,19 +64,19 @@ class SSAGraphBuilder : public ir::Pass {
    *
    * https://en.wikipedia.org/wiki/Hazard_(computer_architecture)#Write_after_read_(WAR)
    */
-  static void PolishGraphToSupportDataHazards(Graph *graph);
+  static void PolishGraphToSupportDataHazards(ir::Graph *graph);
 
-  static VarHandle *CreateOrGetLatestVarHandle(Graph *graph, ir::Node *node,
+  static VarHandle *CreateOrGetLatestVarHandle(ir::Graph *graph, ir::Node *node,
                                                const platform::Place &place,
                                                size_t place_offset);
 
   // Add an output variable (each_var_name, place, place_offset) to op_handle,
   // which belongs to graph
-  static void CreateOpOutput(Graph *graph, OpHandleBase *op_handle,
+  static void CreateOpOutput(ir::Graph *graph, OpHandleBase *op_handle,
                              ir::Node *new_node, const platform::Place &place,
                              size_t place_offset);
 
-  static void AddOutputToLeafOps(Graph *graph);
+  static void AddOutputToLeafOps(ir::Graph *graph);
 };
 }  // namespace details
 }  // namespace framework
diff --git a/paddle/fluid/framework/details/ssa_graph_checker.cc b/paddle/fluid/framework/details/ssa_graph_checker.cc
index 7c79d7f1e881c67514634d56caa715c41927dbce..0438b096109a287366610d06ef2bd14c765a8f43 100644
--- a/paddle/fluid/framework/details/ssa_graph_checker.cc
+++ b/paddle/fluid/framework/details/ssa_graph_checker.cc
@@ -20,7 +20,7 @@ namespace paddle {
 namespace framework {
 namespace details {
 
-bool SSAGraghBuilderWithChecker::IsValidGraph(const Graph *graph) const {
+bool SSAGraghBuilderWithChecker::IsValidGraph(const ir::Graph *graph) const {
   std::unordered_map<OpHandleBase *, size_t> pending_ops;
   std::unordered_set<VarHandleBase *> pending_vars;
   std::unordered_set<VarHandleBase *> ready_vars;
diff --git a/paddle/fluid/framework/details/ssa_graph_checker.h b/paddle/fluid/framework/details/ssa_graph_checker.h
index 2e397e86825a41765a360d31fa8595d17027f3ec..51ce6e5ecad755613551aa6525b5cfbe4a8933ef 100644
--- a/paddle/fluid/framework/details/ssa_graph_checker.h
+++ b/paddle/fluid/framework/details/ssa_graph_checker.h
@@ -28,7 +28,8 @@ class SSAGraghBuilderWithChecker : public SSAGraphBuilder {
       std::unique_ptr<SSAGraphBuilder>&& builder)
       : builder_(std::move(builder)) {}
 
-  std::unique_ptr<Graph> Apply(std::unique_ptr<Graph> graph) const override {
+  std::unique_ptr<ir::Graph> Apply(
+      std::unique_ptr<ir::Graph> graph) const override {
     auto new_graph = builder_->Apply(std::move(graph));
     PADDLE_ENFORCE(IsValidGraph(new_graph.get()));
     return new_graph;
@@ -38,7 +39,7 @@ class SSAGraghBuilderWithChecker : public SSAGraphBuilder {
     return builder_->GetVarDeviceID(var_name);
   }
 
-  bool IsValidGraph(const Graph* graph) const;
+  bool IsValidGraph(const ir::Graph* graph) const;
 
  private:
   std::unique_ptr<SSAGraphBuilder> builder_;
diff --git a/paddle/fluid/framework/details/ssa_graph_printer.cc b/paddle/fluid/framework/details/ssa_graph_printer.cc
index 6dd6fd262e35a192ba85eb3aa16660526d2ebca2..20aab1464400aa9bb1bd6af11c06269c688a8308 100644
--- a/paddle/fluid/framework/details/ssa_graph_printer.cc
+++ b/paddle/fluid/framework/details/ssa_graph_printer.cc
@@ -21,7 +21,7 @@ namespace framework {
 namespace details {
 
 template <typename Callback>
-static inline void IterAllVar(const Graph &graph, Callback callback) {
+static inline void IterAllVar(const ir::Graph &graph, Callback callback) {
   for (auto &each : graph.Get<GraphVars>("vars")) {
     for (auto &pair1 : each) {
       for (auto &pair2 : pair1.second) {
@@ -35,7 +35,7 @@ static inline void IterAllVar(const Graph &graph, Callback callback) {
   }
 }
 
-void GraphvizSSAGraphPrinter::Print(const Graph &graph,
+void GraphvizSSAGraphPrinter::Print(const ir::Graph &graph,
                                     std::ostream &sout) const {
   size_t var_id = 0;
   std::unordered_map<const VarHandleBase *, size_t> vars;
diff --git a/paddle/fluid/framework/details/ssa_graph_printer.h b/paddle/fluid/framework/details/ssa_graph_printer.h
index cd72162f44ca76aa6340606cf79a73601eae89af..a77c1bad3f15bca9064ded860696eb68b033b090 100644
--- a/paddle/fluid/framework/details/ssa_graph_printer.h
+++ b/paddle/fluid/framework/details/ssa_graph_printer.h
@@ -25,12 +25,12 @@ namespace details {
 class SSAGraphPrinter {
  public:
   virtual ~SSAGraphPrinter() {}
-  virtual void Print(const Graph& graph, std::ostream& sout) const = 0;
+  virtual void Print(const ir::Graph& graph, std::ostream& sout) const = 0;
 };
 
 class GraphvizSSAGraphPrinter : public SSAGraphPrinter {
  public:
-  void Print(const Graph& graph, std::ostream& sout) const override;
+  void Print(const ir::Graph& graph, std::ostream& sout) const override;
 };
 
 class SSAGraghBuilderWithPrinter : public SSAGraphBuilder {
@@ -50,7 +50,8 @@ class SSAGraghBuilderWithPrinter : public SSAGraphBuilder {
         stream_ptr_(std::move(sout)),
         stream_ref_(*stream_ptr_) {}
 
-  std::unique_ptr<Graph> Apply(std::unique_ptr<Graph> graph) const override {
+  std::unique_ptr<ir::Graph> Apply(
+      std::unique_ptr<ir::Graph> graph) const override {
     auto new_graph = builder_->Apply(std::move(graph));
     printer_->Print(*new_graph, stream_ref_);
     return new_graph;
diff --git a/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc b/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
index f85c62dd6c4a8033a037b1e001ece6a9cc90ca98..c19f74476f9a1498a7d61f5faf204e9966aea155 100644
--- a/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
+++ b/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
@@ -21,7 +21,8 @@ namespace framework {
 namespace details {
 ThreadedSSAGraphExecutor::ThreadedSSAGraphExecutor(
     const ExecutionStrategy &strategy, const std::vector<Scope *> &local_scopes,
-    const std::vector<platform::Place> &places, std::unique_ptr<Graph> &&graph)
+    const std::vector<platform::Place> &places,
+    std::unique_ptr<ir::Graph> &&graph)
     : graph_(std::move(graph)),
       pool_(strategy.num_threads_ >= 2 ? new ::ThreadPool(strategy.num_threads_)
                                        : nullptr),
diff --git a/paddle/fluid/framework/details/threaded_ssa_graph_executor.h b/paddle/fluid/framework/details/threaded_ssa_graph_executor.h
index bf7c0a367a19ff4ac9462334516f1577672faa68..3d67daa45e20fdea52689684397ad01f2f4cd783 100644
--- a/paddle/fluid/framework/details/threaded_ssa_graph_executor.h
+++ b/paddle/fluid/framework/details/threaded_ssa_graph_executor.h
@@ -40,7 +40,7 @@ class ThreadedSSAGraphExecutor : public SSAGraphExecutor {
   ThreadedSSAGraphExecutor(const ExecutionStrategy &strategy,
                            const std::vector<Scope *> &local_scopes,
                            const std::vector<platform::Place> &places,
-                           std::unique_ptr<Graph> &&graph);
+                           std::unique_ptr<ir::Graph> &&graph);
 
   // Run a SSAGraph by a thread pool
   // Use topological sort algorithm
@@ -53,7 +53,7 @@ class ThreadedSSAGraphExecutor : public SSAGraphExecutor {
              details::OpHandleBase *op);
 
  private:
-  std::unique_ptr<Graph> graph_;
+  std::unique_ptr<ir::Graph> graph_;
   std::unique_ptr<::ThreadPool> pool_;
   std::vector<Scope *> local_scopes_;
   std::vector<platform::Place> places_;
diff --git a/paddle/fluid/framework/ir/graph.cc b/paddle/fluid/framework/ir/graph.cc
index 46640fedcce16079abdebe61bc3c8fb87f8822eb..18211f2e2b0e2b50c51b378f0b36a0ece7d5926f 100644
--- a/paddle/fluid/framework/ir/graph.cc
+++ b/paddle/fluid/framework/ir/graph.cc
@@ -22,6 +22,7 @@ limitations under the License. */
 
 namespace paddle {
 namespace framework {
+namespace ir {
 /*
 namespace {
 void SortHelper(
@@ -41,7 +42,7 @@ void SortHelper(
   ret->push_back(node);
 }
 
-std::vector<ir::Node*> TopologySort(
+std::vector<ir::Node*> TopologySortOperations(
     const std::map<ir::Node *, std::unordered_set<ir::Node *>> &adj_list) {
   std::unordered_set<ir::Node *> visited;
   std::vector<ir::Node *> ret;
@@ -156,7 +157,7 @@ bool HasCircle(const std::map<ir::Node *, std::unordered_set<ir::Node *>>
   return false;
 }
 
-std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildAdjList(
+std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildOperationAdjList(
     const std::vector<ir::Node*> &nodes) {
   std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list;
 
@@ -178,17 +179,17 @@ std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildAdjList(
   return adj_list;
 }
 
-std::vector<ir::Node *> TopologySortOperationFromInToOut(
+std::vector<ir::Node *> TopologySortOperationsOperationFromInToOut(
     const std::vector<std::unique_ptr<ir::Node>> &nodes) {
   std::vector<ir::Node*> tmp;
   for (auto& n : nodes) {
     tmp.push_back(n.get());
   }
   std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list =
-BuildAdjList(tmp);
+BuildOperationAdjList(tmp);
 
   PADDLE_ENFORCE(!HasCircle(adj_list));
-  std::vector<ir::Node*> ret = TopologySort(adj_list);
+  std::vector<ir::Node*> ret = TopologySortOperations(adj_list);
 
   ir::Node *last_backward = nullptr;
   std::vector<ir::Node *> optimize_ops;
@@ -235,5 +236,6 @@ BuildAdjList(tmp);
   return ret;
 }*/
 
+}  // namespace ir
 }  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph.h b/paddle/fluid/framework/ir/graph.h
index b4ac135b029005b723abca2cb9b9a9aa175eda40..a1e39b08a4da703e494dfed87578179bfed17597 100644
--- a/paddle/fluid/framework/ir/graph.h
+++ b/paddle/fluid/framework/ir/graph.h
@@ -26,13 +26,13 @@ limitations under the License. */
 
 namespace paddle {
 namespace framework {
-
+namespace ir {
 class Graph {
  public:
-  explicit Graph(const ProgramDesc& program);
+  explicit Graph(const ProgramDesc &program);
 
   virtual ~Graph() {
-    for (auto& attr : attrs_) {
+    for (auto &attr : attrs_) {
       attr_dels_[attr.first]();
     }
     attrs_.clear();
@@ -40,12 +40,12 @@ class Graph {
   }
 
   template <typename AttrType>
-  AttrType& Get(const std::string& attr_name) const {
-    return *boost::any_cast<AttrType*>(attrs_.at(attr_name));
+  AttrType &Get(const std::string &attr_name) const {
+    return *boost::any_cast<AttrType *>(attrs_.at(attr_name));
   }
 
   template <typename AttrType>
-  void Set(const std::string& attr_name, AttrType* attr) {
+  void Set(const std::string &attr_name, AttrType *attr) {
     PADDLE_ENFORCE(attrs_.count(attr_name) == 0);
     attrs_[attr_name] = attr;
     attr_dels_[attr_name] = [attr, attr_name]() {
@@ -54,17 +54,17 @@ class Graph {
     };
   }
 
-  ir::Node* CreateVarNode(VarDesc* var_desc) {
+  ir::Node *CreateVarNode(VarDesc *var_desc) {
     nodes.emplace_back(new ir::Node(var_desc));
     return nodes.back().get();
   }
 
-  ir::Node* CreateOpNode(OpDesc* op_desc) {
+  ir::Node *CreateOpNode(OpDesc *op_desc) {
     nodes.emplace_back(new ir::Node(op_desc));
     return nodes.back().get();
   }
 
-  ir::Node* CreateEmptyNode(const std::string& name, ir::Node::Type type) {
+  ir::Node *CreateEmptyNode(const std::string &name, ir::Node::Type type) {
     nodes.emplace_back(new ir::Node(name, type));
     return nodes.back().get();
   }
@@ -73,10 +73,10 @@ class Graph {
 
  private:
   // NOTE: program_ shouldn't be exposed to user.
-  const ProgramDesc& program_;
+  const ProgramDesc &program_;
   std::map<std::string, boost::any> attrs_;
   std::map<std::string, std::function<void(void)>> attr_dels_;
 };
-
+}  // namespace ir
 }  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph_helper.cc b/paddle/fluid/framework/ir/graph_helper.cc
index ecd90f4f3ec699298793a58ec3ce3d2d4a41ab03..76458be135018692b1b766dedbadada8340a0423 100644
--- a/paddle/fluid/framework/ir/graph_helper.cc
+++ b/paddle/fluid/framework/ir/graph_helper.cc
@@ -64,7 +64,7 @@ bool HasCircleHelper(
 
 bool HasCircle(const Graph &graph) {
   std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list =
-      BuildAdjList(graph);
+      BuildOperationAdjList(graph);
 
   std::unordered_set<ir::Node *> visited;
   std::unordered_set<ir::Node *> in_trace;
@@ -76,9 +76,9 @@ bool HasCircle(const Graph &graph) {
   return false;
 }
 
-std::vector<ir::Node *> TopologySort(const Graph &graph) {
+std::vector<ir::Node *> TopologySortOperations(const Graph &graph) {
   std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list =
-      BuildAdjList(graph);
+      BuildOperationAdjList(graph);
   std::unordered_set<ir::Node *> visited;
   std::vector<ir::Node *> ret;
   for (auto adj : adj_list) {
@@ -89,7 +89,7 @@ std::vector<ir::Node *> TopologySort(const Graph &graph) {
   return ret;
 }
 
-std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildAdjList(
+std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildOperationAdjList(
     const Graph &graph) {
   std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list;
 
diff --git a/paddle/fluid/framework/ir/graph_helper.h b/paddle/fluid/framework/ir/graph_helper.h
index b8714eb5be03143657c22903b0283af7d76f83bd..55b2e3f5ca67a46d692b409e3bc64793883bb05a 100644
--- a/paddle/fluid/framework/ir/graph_helper.h
+++ b/paddle/fluid/framework/ir/graph_helper.h
@@ -26,9 +26,9 @@ namespace framework {
 namespace ir {
 bool HasCircle(const Graph &graph);
 
-std::vector<ir::Node *> TopologySort(const Graph &graph);
+std::vector<ir::Node *> TopologySortOperations(const Graph &graph);
 
-std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildAdjList(
+std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildOperationAdjList(
     const Graph &graph);
 }  // namespace ir
 }  // namespace framework
diff --git a/paddle/fluid/framework/ir/graph_test.cc b/paddle/fluid/framework/ir/graph_test.cc
index 186047b370c778a43a2828d249716ea0bafee39e..f8fbd2242d5922591c07621a812ccd2531410861 100644
--- a/paddle/fluid/framework/ir/graph_test.cc
+++ b/paddle/fluid/framework/ir/graph_test.cc
@@ -93,7 +93,7 @@ TEST(GraphTest, Basic) {
   ASSERT_EQ(proto::VarType::LOD_TENSOR,
             prog.MutableBlock(0)->Var("test_out")->GetType());
 
-  std::unique_ptr<Graph> g(new Graph(prog));
+  std::unique_ptr<ir::Graph> g(new ir::Graph(prog));
   ASSERT_EQ(g->nodes[0]->Name(), "sum");
   ASSERT_EQ(g->nodes[0]->inputs[0]->Name(), "test_a");
   ASSERT_EQ(g->nodes[0]->inputs[1]->Name(), "test_b");
diff --git a/paddle/fluid/framework/parallel_executor.cc b/paddle/fluid/framework/parallel_executor.cc
index 1e5bba62b53025dacdbf2d74b35f266cf4e422c2..02c836bea194553bb9c4bc5677cc408dd302e9ce 100644
--- a/paddle/fluid/framework/parallel_executor.cc
+++ b/paddle/fluid/framework/parallel_executor.cc
@@ -132,7 +132,7 @@ ParallelExecutor::ParallelExecutor(
 #endif
   }
   builder_ = builder_factory.Create();
-  std::unique_ptr<Graph> graph(new Graph(main_program));
+  std::unique_ptr<ir::Graph> graph(new ir::Graph(main_program));
   graph = builder_->Apply(std::move(graph));
   member_->executor_.reset(new details::ThreadedSSAGraphExecutor(
       exec_strategy, member_->local_scopes_, places, std::move(graph)));