I want to throw some cold water on this notion because it’s dangerously appealing. When I was doing my PhD in graph theory I had a similar feeling that graphs were everything, but this is a more general property of mathematics. Graphs are appealing to a certain kind of thinker, but there is nothing so special about them beyond their efficacy at modeling certain things and many isomorphic models are possible. In particular they admit helpful visualizations but they are ultimately no more powerful (or any less powerful!) than many equivalent mathematical models. I just worry from the tone of your post you might be overvaluing graphs so I’d like to pass down my wisdom that they are valuable but not especially valuable in general.
I want to throw some cold water on this notion because it’s dangerously appealing. When I was doing my PhD in graph theory I had a similar feeling that graphs were everything, but this is a more general property of mathematics. Graphs are appealing to a certain kind of thinker, but there is nothing so special about them beyond their efficacy at modeling certain things and many isomorphic models are possible. In particular they admit helpful visualizations but they are ultimately no more powerful (or any less powerful!) than many equivalent mathematical models. I just worry from the tone of your post you might be overvaluing graphs so I’d like to pass down my wisdom that they are valuable but not especially valuable in general.
Oh lord no, this is just a bunch of random applications. Though I’ve also seen the failure mode you describe, so good warning.
Convex optimization, though. That’s everything.