Algebraic interplay between renormalization and monodromy

We investigate combinatorial and algebraic aspects of the interplay between renormalization monodromies for Feynman amplitudes. clarify how extraction subgraphs from a graph interacts with putting edges onshell or contracting them to obtain reduced graphs. Graph by this leads study cointeracting bialgebras. One bialgebra comes hence is needed renormalization. The other an incidence put either on- offshell. It related multivalued function which renormalized evaluates. Summing over infinite series graphs, consequences Green functions are derived using Dyson--Schwinger equations.