std::unordered_map<tensorflow::string, tensorflow::Node*> name_map
      TF_GUARDED_BY(mu);

  // The keys of this map are all the active sessions using this graph. Each
  // value records whether the graph has been mutated since the corresponding
  // session has been run (this is detected in RecordMutation function). If the
  // string is empty, no mutation has occurred. Otherwise the string is a