One naively thinks of (continuous) functions as of graphs1 (lines drawn in a 2-dimensional coordinate space).
One often thinks of (countable) graphs2 (vertices connected by edges) as represented by adjacency matrices.
That's what I learned from early on, but only recently I recognized that the "drawn" graphs1 are nothing but generalized - continuous - adjacency matrices, and thus graphs1 are more or less the same as graphs2.
I'm quite sure that this is common (maybe implicit) knowledge among working mathematicians, but I wonder why I didn't learn this explicitly in any textbook on set or graph theory I've read. I would have found it enlightening.
My questions are:
Did I read my textbooks too superficially?
Is the analogy above (between graphs1 and graphs2) misleading?
Or is the analogy too obvious to be mentioned?