I'm a visual/spatial thinker, which is one of the reasons I heavily drawn to Graph Theory. However, I am struggling to learn about the concept of "warmth", and after checking multiple papers, the most promising definition was found here. It starts off with nice description of random-walk, but then quickly swerves to graph homeomorphisms before I got my bearings.
Specifically, I am unclear how they color this walk, or how this $d-walk$ works on non-regular graphs. I realize that afterwards I'll have to bite the bullet and read the nitty-gritty stuff, but I find that prefacing my learning with an intuitive understanding/context helps me in digesting everything.
Update: I tried skimming the later stuff to see if that would help, and now also want clarify if in the beginning of Section 2, the statement "we must show that $Hom(T^d,K_d)$ is not cold" was a typo, as to my understanding it should be $Hom(T^{d-2},K_d)$ instead.