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The loop order of a connected Feynman diagram is the number $L=I-V+1$ of independent momentum cycles, where $I$ is the number of internal lines and $V$ the number of vertices. Each loop introduces an unconstrained momentum integral.

A one-particle-irreducible Feynman diagram is a connected Feynman diagram that remains connected after any one internal line is cut. The vertices of the quantum effective action generate precisely these diagrams.