What is transitivity property of digraph?

Question

I'm studying discrete structures following the MIT lecture (Mathematics for Computer Science). In the book, the definition of transitivity is as follow:

Then the book says the graph in Figure 7.8 below does not satisfy the transitivity property:

But I think it is already transitive in Figure 7.8 as v2 -> v3 and v3 -> v4, then v2 -> v4.

Would anybody help me understand what I am missing here? Thank you so so so much in advance!!!

• All the pictures are from the course note.

Answer 1

The first figure is not a transitive relation but figure 7.8 is a transitive relation.

The first Figure is not transitive since we have v1-->v2 and v2-->v3 but we don't have v1-->v3 But Figure 7.8 shows us how to change the first figure to make a transitive relation.