I am confused about the time complexity of the Boost Graph function vertex() when operating on an adjacency_list.

This page in the manual appears to claim that the function vertex() runs in constant time even when template parameter VertexList is listS.

• vertex()
  This operation is constant time for vecS and for listS.

However, it is a mystery to me how the function can achieve constant time operation when the underlying data structure is a std::list. I have looked at the generated object code and it looks like the function vertex() compiles to an iterative loop when VertexList=listS, versus a constant lookup when VertexList=vecS.

Finally, I created a small test program which confirms that the run time scales with the value of the index passed to vertex() when using listS.

How does this add up?
Is there some special way to make vertex() run in constant time, or did I misunderstand the documentation, or is the documentation simply wrong?