Graphs and Feynman diagrams: common properties?

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I would like to know whether it is possible to establish a clear parallelism between the main features of graph theory (connected and disconnected graphs, graphs with loops, etc) and the 5 basic types of Feynman diagrams (connected is an obvious case,and I guess so is irreducible....but what about sef-energy graphs, skeleton graphs, etc???).

Thanks in advance