Ironically, I think you failed to comprehend the article. Adjacency matrices (which you are presumably referring to, but were not mentioned in the article) are neither efficient nor algebraicly convenient. No one represents graphs as matrices in computer science, and graph theorists rarely touch representation theory. It's not that useful when the natural representations are normally much simpler and easier to work with.
Not sure it's fair to say that graph theorists rarely use matrices to represent graphs: for many problems in graph theory some of the simplest solution involves representing the graph as a matrix (eg Hoffman-Singleton theorem).
> No one represents graphs as matrices in computer science, and graph theorists rarely touch representation theory.
Are you conflating linear algebra and representation theory, or did you really mean to refer to representation theory in particular? The notion of a quiver (https://en.wikipedia.org/wiki/Quiver_(mathematics) ) seems to me to be a unification of the two fields; I'm not a graph theorist, but I have a hard time imagining that they don't at least consider these structures.
Oh, yes, we should definitely draw lessons from academic mathematicians about what is accessible and convenient to understand. THAT's a field that's never had a problem connecting to laymen.
