Draw some dots and connect them with lines; this is a graph. Not a graph of a function as in calculus, but a combinatorial graph. Such graphs are defined purely structurally, and many things can be proved using that point of view. But bigger and better things can be done when we bring in other parts of mathematics. I will introduce some basic linear algebra and show how it codifies some properties of graphs. I will focus on a class called strongly regular graphs which are particularly appropriate for this approach.