The word “graph” has multiple, unrelated, meanings in mathematics. What we’re concerned with here is not graphs of functions but rather graphs as they are understood in the field known, appropriately enough, as graph theory. A graph is a set of vertices and edges. The edges connect vertices. There are, in fact, two different ways to make this notion precise, depending on whether we regard the connections between vertices to have a direction or not. These are called directed graphs and undirected graphs.