Feynman diagrams [and networks]

In the standard approach to particle physics, possible interaction processes are represented by networks in which each node corresponds to an elementary interaction, and the nodes are joined by connections which correspond to the propagation of particles in spacetime. I can see no direct physical relationship between such diagrams and the networks I consider. However, at a mathematical level, the set of trivalent networks with n nodes formally corresponds to the set of n^th order Feynman diagrams in a ϕ³ field theory. (Compare page 1039.)