I have found the same vertex-edge graph in two seemingly disparate places and am wondering about any possible connection between the two (beyond just pure coincidence, of course).
The relevant Feynman diagram is one of the quartic $\phi^4$ interactions (one loop, two external legs) found on the Wikipedia page about Quantum Field Theory:
And the other is in a paper "Laplacians On The Basilica Julia Set":
where this so-called "arc-type cell" is, roughly speaking, a graph-version of a first-order approximation of the upper boundary of the root basin (basin around $0$) of the "basilica" Julia set of $z_{n+1}=z_n^2-1$, (red emphasis is mine):
0th and 1st order approximations of basilica set:
Is this just a structural coincidence? And does this have anything to do with renormalization?