[hnfong]

GP says "graphs can be conveniently represented as matrices", which I believe is totally correct.

The GP's claim that graphs (not matrices) are equivalent to edge lists is almost correct. The textbook definition of graphs is G = (V, E) , where V are the set of vertices and E are the set of edges. Implicitly E contains relationships between some of the vertices, so the only thing in the V which isn't part of an edge in E are vertices that are not related to any edge. So if you have a connected graph, you can unambiguously define it by way of a set of edges (~= "edge lists") without explicitly mentioning the vertices.

In short, I don't see any fundamental error in GP's quoted sentence unless you're trying to be extra pedantic.