Functions, graphs, and adjacency matrices 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?


My opinion: the analogy is not misleading, is not too obvious to be mentioned, but is also not terribly useful. Have you found a use for it? 
EDIT: Here's another way to think about it. A $\it relation$ on a set $S$ is a subset of $S\times S$, that is, it's a set of ordered pairs of elements of $S$. A relation on $S$ can be viewed as a (directed) graph, with vertex set $S$ and edge set the relation. We draw this graph by drawing the vertices as points in the plane and the edges as (directed) line segments connecting pairs of points
Now consider "graph" in the sense of "draw the graph of $x^2+y^2=1$." That equation is a relation on the set of real numbers, and the graph is obtained by drawing the members of this relation as points in the plane. 
So the two kinds of graph are two ways of drawing a picture to illustrate a relation on a set. 
