We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes.We focus on the interplay between graph homology, Hopf-algebraic structures on Feynman graphs and the analytic structure of their associated integrals.Furthermore, we discuss the appearance of cubical complexes where the differential is formed by reducing internal edges and by putting edgepropagators on the mass-shell.
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Berghoff et al. (2023) studied this question.