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   367     }  | 
   367     }  | 
   368   | 
   368   | 
   369     /* stream operations, for testing purpose */  | 
   369     /* stream operations, for testing purpose */  | 
   370   | 
   370   | 
   371     friend std::ostream& operator<<(std::ostream& os, const Node& i) {  | 
   371     friend std::ostream& operator<<(std::ostream& os, const Node& i) {  | 
   372       os << i.node->id; return os;   | 
   372       if (i.valid())  | 
         | 
   373 	os << i.node->id;   | 
         | 
   374       else  | 
         | 
   375 	os << "invalid";  | 
         | 
   376       return os;   | 
   373     }  | 
   377     }  | 
   374     friend std::ostream& operator<<(std::ostream& os, const Edge& i) {  | 
   378     friend std::ostream& operator<<(std::ostream& os, const Edge& i) {  | 
   375       os << "(" << i.edge->_tail->id << "--" << i.edge->id << "->" << i.edge->_head->id << ")";  | 
   379       if (i.valid())   | 
         | 
   380 	os << "(" << i.edge->_tail->id << "--" << i.edge->id << "->" << i.edge->_head->id << ")";  | 
         | 
   381       else   | 
         | 
   382 	os << "invalid";  | 
   376       return os;   | 
   383       return os;   | 
   377     }  | 
   384     }  | 
   378   | 
   385   | 
   379     class Node { | 
   386     class Node { | 
   380       friend class ListGraph;  | 
   387       friend class ListGraph;  |