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We use the Hopf algebra structure of the time-ordered algebra of fieldoperators to generate all connected weighted Feynman graphs in a recursive andefficient manner. The algebraic representation of the graphs is such that theycan be evaluated directly as contributions to the connected n-point functions.The recursion proceeds by loop order and vertex number.Comment: 22 pages, LaTeX + AMS + eepic; new section with alternative recursion  formula added, further minor changes and correction

Generating loop graphs via Hopf algebra in quantum field theory