What are the various kinds of graphs that can be defined on \$C(X)\$

I was considering the space $$C(X)$$ where $$X$$ is a topological space and $$C(X)$$ is the set of all continuous functions from $$X$$ to $$\Bbb R$$.

What are the various kinds of graphs that can be defined on them?

One possible graph is $$f\sim g\iff fg=0$$ which is commonly known as zero divisor graph.

What are other ways where we can utilize properties of $$C(X)$$ to find graph theoretic properties?

Can someone kindly direct me to some possible research going on in this direction and maybe also provide some research links?

Thank You.