  We demonstrate that the fundamental algebraic structure underlying the
Connes-Kreimer Hopf algebra -- the insertion pre-Lie structure on graphs --
corresponds directly to the canonical pre-Lie structure of polynomial vector
fields. Using this fact, we construct a Hopf algebra built from tensors that is
isomorphic to a version of the Connes-Kreimer Hopf algebra that first appeared
in the perturbative renormalization of quantum field theories.
