  The study of Feynman rules is much facilitated by the two Symanzik
polynomials, homogeneous polynomials based on edge variables for a given
Feynman graph. We review here the role of a recently discovered third graph
polynomial based on half-edges which facilitates the transition from scalar to
gauge theory amplitudes: the corolla polynomial. We review in particular the
use of graph homology in the construction of this polynomial.
