Almost every time I've implemented a graph algorithm professionally, it's been using matrix operations because they came with a GPU implementation and smashed t

Almost every time I've implemented a graph algorithm professionally, it's been using matrix operations because they came with a GPU implementation and smashed the performance of a naive implementation. But from a design and theory standpoint, I prefer to work independent of the representation as much as possible, and only switch in the matrix language as an implementation of a type in already working code. (Sometimes, this isnt quite possible and you need to, eg, reorder operations to make it efficient to calculate in your representation.) So I would say that linear algebra is a big deal for implementations, if not as much of one theoretically. (Mostly cause my computer has really fast linear algebra chips/code, and not so much for random graph traversal.)