Consider the graph shown in Figure 9.19.

Let us imagine that the vertices are towns and the edges are roads connecting them. It is clear that we can travel from a to B by road but there is no such roadway between D and H. To reach B from a, we take the following route:

Figure 9.19.

Naturally, we may represent the above route as . Further, is also a route between A and B. is also a route, perhaps roundabout, between A and B. Let us also note that is not a meaningful route at all, for E is not an end of e₆. We formalize the idea of a route, called a walk, in the following definition.