How to parse tree graphs correctly?

Question

PHP

Greetings. I drew a graph here on the blocks.js

library. As a result, I have 2 arrays. One is the blocks themselves and their description, the other is the links between the blocks.
I want to build logic according to the drawn graph, more precisely, that the logic would be generated based on the drawn graph. Tell me where to start, what to study, what steps need to be done here? I don’t know how to google it ...
I want to parse on the PHP backend