Dirk Kreimer and Alain Connes have developed a Hopf algebraic description of the process of renormalization in quantum field theory. Their starting point is the definition of a certain algebra structure on the space of all (Feynman-)graphs. The definition can be found, for instance, in equation (6) of http://arxiv.org/abs/hep-th/0510202 . I suspect that this algebra is most elegantly expressed as the "multicategory algebra" of the obvious multicategory of (Feynman-)graphs. This multicategory should be the obvious slight generalization of example 4.2.14 in Tom Leinster's book http://arxiv.org/abs/math.CT/0305049 . Here by "multicategory algebra" I mean a generalization to multicategories of the concept "category algebra" or "path algebra" of an ordinary category. I.e. the algebra generated by the morphisms in the category with the product derived from the composition law in the category. (Hence, in particular I am *not* referring to the concept "algebra *for* a multicategory" as in "algebra for an operad", discussed in section 4.3 of Leinster's book.) I would think such a concept of a multicategory(-path-)algebra should exist and should be given by the obvious generalization of formula (6) in the above cited paper. This concept seems to be so natural that I expect it must have been considered before. If so, could anyone point me to relevant sources?