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.