Can a visitor modify properties in a graph?  I would like to use the following visitor with the breadth_first_search algorithm:

 struct ExecPriorityVisitor : public boost::default_dfs_visitor
 {
   ExecPriorityVisitor();
   void start_vertex( Vertex v, Graph& g ){ g[v].priority = 0; }
   void examine_edge( Edge e, Graph& g ){
     const Vertex src  = boost::source(e,g);
     Vertex dest = boost::target(e,g);
     int& priority = g[dest].priority;
     priority = std::max( priority, g[src].priority + 1 );
   }
 };

However, it fails to compile because apparently the graph argument must be const.  That implies that I cannot modify graph properties from within the visitor?  Why not?