  A non-commutative, planar, Hopf algebra of rooted trees was proposed in L.
Foissy, Bull. Sci. Math. 126 (2002) 193-239. In this paper we propose such a
non-commutative Hopf algebra for graphs. In order to define a non-commutative
product we use a quantum field theoretical (QFT) idea, namely the one of
introducing discrete scales on each edge of the graph (which, within the QFT
framework, corresponds to energy scales of the associated propagators).
