I did not manage to incorporate the Vietoris-Rips with the PersistentHomology WFR, however, after reading the following article, I figured I could use the NearestNeighbor function to build something that works like Vietoris-Rips.
Manipulate[
NearestNeighborGraph[positions, k], {k, 1, 1, 1}]
Make sure to set positions as your set of {x,y} coordinates. Sadly, the functions does not work if I'm using too many coordinates, but that might be on my hardware. The function also only works using whole numbers.
