I agree that for describing a specific graph, drawing it is sometimes the best way. Most of the time an automaton or graph is a mathematical object under study.

I agree that for describing a specific graph, drawing it is sometimes the best way. Most of the time an automaton or graph is a mathematical object under study. The notation used to study graphs and automatons and prove things about them is symbolic. Saying that maths notation is visual because a mathematician might draw a diagram to illustrate their proof is like saying that programming is already visual because a programmer might draw a diagram to illustrate their program. It's true that there are some visual notations in mathematics, but they tend to be the exception rather than the rule, and where they are used it's a mixed system most of the time. Frege's notation was half symbolic half visual, and the visual part of it didn't catch on except for the horizontal line. The rest of it got "symbolified". I don't think that's a coincidence. Actually the most commonly used half visual half symbolic notation in mathematics is the commutative diagram. I suspect that over time even the use of those may decrease in favour of symbolic type theory notation. I do think some sprinkling of visual notation is useful, also in programming, but representing expression trees as dataflow graphs? That has been tried many times and it hasn't been successful, nor is it likely to be in the future. I don't think flat text has any future though. A program has structure and is not best represented as an array of characters. Symbols and nested syntax are here to stay however. Humans just deal better with nesting and symbolic references than with a forest of lines and arrows.