2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189813We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number.22 pages, LaTeX + AMS + eepic; new section with alternative recursion formula added, further minor changes and correctionsMathematical PhysicsHigh Energy Physics - TheoryCombinatoricstext