///of the shortest path tree,

     ///of the shortest path tree,

     ///i.e. it returns the last edge of a shortest path from the root(s) to \c

     ///i.e. it returns the last edge of a shortest path from the root(s) to \c

     ///v. It is \ref INVALID

     ///v. It is \ref INVALID

     ///if \c v is unreachable from the root(s) or \c v is a root. The

     ///if \c v is unreachable from the root(s) or \c v is a root. The

     ///shortest path tree used here is equal to the shortest path tree used in

     ///shortest path tree used here is equal to the shortest path tree used in

     ///\pre Either \ref run() or \ref start() must be called before using

     ///\pre Either \ref run() or \ref start() must be called before using

     ///this function.

     ///this function.

     ///\todo predEdge could be a better name.

     ///\todo predEdge could be a better name.

     Edge pred(Node v) const { return (*_pred)[v];}

     Edge pred(Node v) const { return (*_pred)[v];}

     ///i.e. it returns the last but one node from a shortest path from the

     ///i.e. it returns the last but one node from a shortest path from the

     ///root(a) to \c /v.

     ///root(a) to \c /v.

     ///It is INVALID if \c v is unreachable from the root(s) or

     ///It is INVALID if \c v is unreachable from the root(s) or

     ///if \c v itself a root.

     ///if \c v itself a root.

     ///The shortest path tree used here is equal to the shortest path

     ///The shortest path tree used here is equal to the shortest path

     ///\pre Either \ref run() or \ref start() must be called before

     ///\pre Either \ref run() or \ref start() must be called before

     ///using this function.

     ///using this function.

     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:

     Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:

 				  G->source((*_pred)[v]); }

 				  G->source((*_pred)[v]); }